with reference initially to fig1 , there follows a description of a first aspect of the intervertebral disk prosthesis . in this figure , there is shown in simplified manner a first vertebra v 1 and a second vertebra v 2 between which the intervertebral disk prosthesis 10 is to be put into place . the prosthesis 10 is constituted by a first prosthesis element 12 and a second prosthesis element 14 , and by a first fixing element 16 and a second fixing element 18 . the prosthesis element 12 has a cooperation face 12 a and an active face 12 b also referred to as a rubbing face or a contact face . this face 12 b is in the form of a convex spherical cap . the prosthesis element 14 also has an active face or contact face 14 b which is in the shape of a concave spherical cap and which is naturally designed to cooperate with the active surface 12 b of the prosthesis element 12 . as explained in greater detail below , the radii of curvature of the spherical caps 12 b and 14 b are not identical . the prosthesis element 14 also has a cooperation face 14 a . the fixing element 16 presents a cooperation face 16 a and an anchoring face 16 b . the anchoring face 16 b is provided with any suitable anchoring member 22 for fixing the fixing element 12 to the plate of the vertebra v 1 . the cooperation face 16 a of the fixing element 16 is provided with fasteners that cooperate with complementary fasteners of the face 12 a of the prosthesis element 12 to fasten the prosthesis element to the fixing element , at least in a horizontal plane . similarly , the fixing element 18 has a cooperation face 18 a and an anchoring face 18 b provided with an anchoring member 24 . it will be understood that in this first aspect of the invention , because the prosthesis elements proper and the fixing elements are distinct parts , it is easier to put the intervertebral disk prosthesis into place between the vertebrae while nevertheless ensuring that it is properly secured to the vertebrae . it will also be understood that since each prosthesis element has an active face in the form of a spherical cap , the ball - and - socket type mobility between the two vertebrae is indeed recreated . reference is now made to fig2 a and 2b for describing the intervertebral disk prosthesis in its second aspect . in these figures , there can be seen the vertebrae v 1 and v 2 between which the prosthesis is to be put into place . the prosthesis is constituted by a first prosthesis element 12 ′ and by a second prosthesis element 14 ′. each prosthesis element 12 ′ and 14 ′ is constituted by two distinct parts referenced 26 and 28 for the prosthesis element 12 ′ and 30 and 32 for the prosthesis element 14 ′. each part forming the prosthesis elements has both a fixing face referenced a , and an active face referenced b . the fixing faces a of the parts 26 to 32 are provided with fasteners for engaging the vertebrae v 1 and v 2 , these fasteners possibly being constituted by separate parts , as explained below and as shown in fig1 . the active faces a of the parts constituting the prosthesis elements are defined in such a manner that they form portions of spherical caps that are respectively concave and convex . when the parts 26 and 28 forming the prosthesis element 12 ′ are put into place on the vertebra v 1 , their active faces a are disposed on a concave spherical cap c . similarly , the active faces a of the parts 30 and 32 forming the prosthesis element 14 ′ are disposed on a spherical cap c ′. as mentioned above , these spherical caps c and c ′ may have different radii of curvature . it will be understood that because the two parts constituting the same prosthesis element together constitute a friction or contact surface that is in the form of a spherical cap , the same ball - and - socket mobility is obtained as in fig1 . in addition , because each prosthesis element is constituted by two distinct parts , it will be understood that it is easier for the surgeon to put the prosthesis element into place between the vertebrae . with reference to fig3 , 4 , and 5 , a first embodiment of the intervertebral disk prosthesis is described . in fig3 a and 3b , there can be seen a fixing element referenced 40 . the fixing element 40 is constituted by a plate 42 having an anchoring face 42 b provided with two transverse ribs 44 and 46 which constitute parts for anchoring in a vertebra . the cooperation face 42 a of the plate 42 is fitted with two locking members for locking to the prosthesis element . each of the locking members 48 and 50 is constituted by a strip 54 extending parallel to the ribs 44 . the right section of each strip 54 is generally t - shaped , the strip comprising two flanges 56 and 58 in its portion that is furthest from the plate 42 . in addition , in order to enable the strips to deform elastically to a certain extent , each of them has a longitudinal slot 60 . in fig4 a , 4 b , and 4 c , there can be seen a prosthesis element 62 which is constituted by two separate parts 64 and 66 . the active faces b of the parts 64 and 66 constitute portions of a spherical cap . thus , as explained above , when the parts 64 and 66 are fixed on a vertebra , the spherical cap portions b lie on the same spherical surface . the cooperation face a of each part 64 and 66 includes an anchoring groove 68 over a fraction of its length , the right section of the groove being generally t - shaped and being dimensioned to be capable of receiving the anchoring members 48 and 50 . the grooves 68 extend over a fraction only of the length of the parts 64 and 66 corresponding to the length of the anchor parts 48 and 50 . in addition , and preferably , the cooperation faces a of the parts 64 and 66 include respective setbacks 70 and 72 such that when these parts are fixed on a vertebra , the plate 42 of the fixing element 40 penetrates fully into said setback . as can be seen in fig4 c , the grooves 68 open out via their ends 68 a into end faces of the parts 64 and 66 so as to enable the locking members 48 and 50 to be inserted into the fixing element 40 . naturally , the prosthesis as a whole has a second fixing part 40 ′ identical to the part 40 and a second prosthesis element 62 ° which differs from the prosthesis element 62 solely by the fact that its active surface b defines a spherical cap that is concave . fig4 shows the two prosthesis elements constituted by the parts 64 and 66 and two other analogous parts mounted on the fixing elements 40 and 40 ′. it can be seen that the fixing elements 40 and 40 ′ in this embodiment serve not only the fix each prosthesis element to the corresponding vertebra , but also to position the two parts constituting the same prosthesis element in such a manner that their active surface does indeed constitute a spherical cap . fig1 shows a variant of the first embodiment of the intervertebral disk prosthesis suitable for correcting a tendency to scoliosis . in this variant , when the prosthesis elements 64 ′ and 66 ′, and the fixing elements 40 and 40 ′ are assembled together , the plates 42 of the fixing elements form between them an angle a . in order to obtain this result , the cooperation faces a of the parts 64 and 66 forming the prosthesis element 62 are disposed in a plane pp ′, p 1 p 1 ′ which is not orthogonal to the common axis xx ′ of the spherical caps c and c ′ which are constituted by the active faces of the prosthesis elements . with reference now to fig6 , 7 , and 8 , there follows a description of a second embodiment of the intervertebral disk prosthesis . in this second embodiment , each prosthesis element is constituted by a single part and each prosthesis element is fixed to the corresponding vertebra by a separate fixing element . fig6 a and 6b show an embodiment of the fixing element 80 . the fixing element 80 is constituted by a preferably rectangular plate 82 that is relatively massive . the anchoring face 82 b of the plate 82 is provided with members for anchoring in the vertebra constituted , for example , by two ribs 84 and 86 identical to those fitted to the fixing element 40 shown in fig3 . as explained below , other anchoring elements could be used . as shown in fig6 b , the cooperation face 82 a is provided with a locking groove 88 . this locking groove has an insertion first portion 90 opening out into a long side of the plate 82 and a locking portion 92 which extends parallel to the long direction of the plate 82 . as shown in fig6 a , the groove 88 has a right section that is t - shaped . naturally , the complete prosthesis has a second fixing element 80 ′. fig7 a , 7 b , and 7 c show the prosthesis elements of the prosthesis constituting the second embodiment . the prosthesis element 100 is constituted by a massive part whose cooperation face a presents a shoulder 102 defining a setback portion 104 with the length of the setback portion 104 corresponding to the width of the plate 82 of the fixing element 80 . a locking member 106 projects from the setback portion 104 . the shoulder 102 corresponds to the thickness of the plate 82 . this locking member which is preferably circularly symmetrical about the axis xx ′ is constituted by a head 108 and a body 110 . the diametral section of the locking member 108 is of a shape which corresponds to the shape of the t - groove 88 formed in the plate 82 of the fixing element 80 . the active or contact face b of the prosthesis element 100 comprises a substantially plane portion 112 and a portion 114 in the form of a concave spherical cap . the second prosthesis element 120 is identical to the prosthesis element 100 with the exception of its active face b which comprises a substantially plane portion 122 and a portion in the form of a convex spherical cap 124 suitable for cooperating with the concave spherical cap 114 of the prosthesis element 100 . in fig8 , there can be seen the prosthesis elements 100 and 120 mounted on the two fixing elements 80 and 80 ′. as can be seen more clearly in this figure , in the assembled position , the prosthesis elements 100 and 120 are orthogonal to the fixing elements 80 and 80 ′. fig9 shows a variant embodiment of the anchoring element provided on the anchoring faces of the fixing elements 80 or 40 . in this embodiment , the anchoring elements given general reference 130 is constituted by two projecting triangular parts 132 and 134 each having one of its short sides connected to the short side of the other triangle to form an edge 136 , the angle between the triangles 132 and 137 being less than 180 degree . this method of anchoring serves to prevent any displacement in the planes of the vertebral plates . in fig1 , there can be seen another variant embodiment of the anchoring element which is in this particular case consists in four generally cylindrical studs 140 terminating in conical portions . this figure also shows that the locking members 48 and 50 of the fixing element 40 are preferably spaced further apart than the locking members 48 ′ and 50 ′ of the fixing element 40 ′. this makes it possible for the two fixing elements 40 and 40 ′ to be placed in the configuration shown in the figure . the total thickness of the assembly constituted by the two fixing elements is thus reduced , thereby enabling them to be inserted simultaneously between the two vertebrae . the description above relates to two embodiments of the intervertebral disk prosthesis of the invention , together with variants thereof . as mentioned above , one of the advantages of these prostheses is that they can be put into place using a posterior technique . with reference initially to fig1 a and 12b , there follows a description of the method of putting the prosthesis shown in fig3 , 4 , and 5 into place by the posterior technique . as in the conventional posterior technique for putting intervertebral cages into place , the surgeon begins by providing posterior access to the vertebrae between which the prosthesis is to be placed : the surgeon must also move the two vertebrae apart and remove the natural disk . thereafter , the surgeon usually performs certain resections of portions of the two vertebrae onto which the prosthesis is to be fixed . these resections relate essentially to the epiphysis and to the facets of the vertebrae . functionally , the major resections are those enabling the fixing elements to be anchored to the vertebrae where that is necessary . these resections performed in the vertebral plate are of a shape that is adapted to the anchoring elements with which the fixing elements are fitted . for the rib - shaped fixing elements ( fig3 and 6 ), these resections consist in slots f 1 and f 2 formed in the posterior portions of the vertebral plates ( fig1 a ). for anchoring elements in the form of pegs ( fig1 ), the resections are in the form of holes t 1 , t 2 , . . . pierced in the vertebral plate ( fig1 b ). in other circumstances there is no anchoring element proper . fig1 a to 13g show a vertebral disk prosthesis of the shape shown in fig3 to 5 being put into place . initially , the bottom fixing element 40 ′ is inserted between the vertebrae v 1 and v 2 via their posterior portions ( fig1 a ) from one side or the other of the dura mater . then the fixing element 40 ′ is pushed to go around the spinal cord ( dura mater ) ( fig1 b ) by pivoting and come into position in such a manner that the anchoring ribs are in register with the slots f 1 and f 2 ( fig1 c and 13d ), after which the anchoring ribs are pushed into the slots f 1 and f 2 ( fig1 e ). the same process is used for putting into place the upper fixing element 40 under the upper vertebra v 1 . as shown in fig1 , it is also possible to introduce two fixing elements simultaneously between the vertebrae and then to put them into place separately in the resections . still using the posterior technique , the parts 64 and 64 ′ constituting the right - hand portions of the prosthesis elements are put into place around the right - hand side of the dura mater , going around the spinal cord . the fastening grooves 68 are engaged on the ends of the fastening strips 48 of the fixing elements . this engagement is made possible by the ability of the strips 48 to deform . the prosthesis elements are pushed until the plates 42 of the fastening elements 40 , 40 ′ penetrate into the setbacks 72 of the prosthesis parts 64 ( fig1 g ). finally , the same operation is performed on the parts 66 of the prosthesis elements by engaging them via the left side of the dura mater . fig1 a shows fixing elements being inserted when they are implemented as shown in fig1 . fig1 b shows subsequent placement of the prosthesis elements . fig1 a to 15c show the main steps in putting the intervertebral disk prosthesis shown in fig8 into place . fig1 a shows the bottom fixing element 80 ′ being put into place by being engaged using the posterior technique around one side of the dura mater , after which this part is turned so as to put into position beyond the dura mater . this operation ends with anchoring ribs being inserted into the slots f 1 , f 2 . fig1 a also shows in “ symbolic ” manner the upper fixing element 80 put into place . fig1 b shows the initial stage of putting the prosthesis elements 100 and 120 into place . in this stage , the prosthesis elements are inserted between the vertebrae on one side of the spinal cord , moving in their long direction . the locking members 106 are presented to the inlets to the first portions 90 of the locking grooves 88 in the fixing elements until they come into abutment . thereafter ( fig1 c ), the surgeon pushes the prosthesis elements sideways so that the locking members 106 come into abutment at the ends of the second portions 92 of the locking grooves 88 . the prosthesis elements are locked to the fixing parts by cooperation between the shoulders 102 and the edges of the fixing elements . as explained above , an important advantage of the intervertebral disk prosthesis is that it can be put into place by the posterior technique . nevertheless , this prosthesis can naturally also be put into place by the anterior technique . fig1 a to 16c show the prosthesis shown in fig5 being put into place by the anterior technique , and fig1 a to 17b show the prosthesis shown in fig8 being put into place by the anterior technique . firstly , it should be observed that the slots f ′ 1 and f ′ 2 are adapted to anterior placement so they open out into the periphery of the vertebral plate ( fig1 a ). thereafter , the fixing elements 40 and 40 ′ are put into place between the vertebrae and inserted into the slots f ′ 1 and f ′ 2 . finally , the parts 26 , 28 , 30 , and 32 forming the prosthesis elements are put into place on the fixing elements 40 and 40 ′. fig1 a shows fixing elements 80 and 80 ′ being put into place by the anterior technique , and fig1 b shows the prosthesis elements 100 and 120 being put into place on the fixing elements .