in all the accompanying drawings , the variation of the shortest and the longest total transmission ratio is shown as curves a and b , and the variation of the rpm at lower and higher speed is shown as curves c and d . further , the variation of the gas pedal position fpw is shown under the seed vs . rpm chart as a function of the vehicle speed v for downshift at lower and higher speed , with curve e being for lower speed and curve f , for higher speed . as shown in fig1 , with a vehicle having an infinitely variable transmission , variation is flat after downshift to a desired rpm . the downshift is carried out from a certain gas pedal position is apparent in the figure . hereby , due to the flat course of the rotational speed g without the acceleration mode as a function of the speed , it will not provide the driver with a sporty impression . during a steep course of the rotational speed as function of the speed or , as the case may be , during a steep rotational speed gradient according to the state of the art a compromise between the gradient and the rotational speed level becomes necessary , as can be observed in fig2 , since the target rotational speed can turn out to be too high , especially during a downshift at high speeds ; on the other hand , the target rotational speed can be very low at slow speeds . this is due to the fact that the target rotational speed at low speeds must be low and at high speeds must be high to achieve a desired steep rotational speed gradient . according to the invention , an acceleration mode is suggested within the framework of which after a downshift the rotational speed development will be continued as a function of the speed with a calibrated rotational speed gradient . here the rotational speed gradient will preferably be defined by the gas pedal value and the vehicle speed at the start of the acceleration mode . the acceleration mode is the object of fig3 . here , after the downshift has taken place , a flat rotational speed course g , not represented in fig1 , will be aimed for ; the rotational speed increases with the increasing speed according to the calibrated gradient such that a sporty impression is created . from the comparison of the downshifts shown in the fig1 , it becomes apparent that a substantially broader rotational speed range will be required for reaching a certain speed . within the scope of the advantageous development of the invention shown in fig4 , a gas pedal dependent maximum rotational speed is provided in the acceleration mode such that unacceptable or , as the case may be , too high rotational speeds will be avoided . with increasing speed and decreasing difference between the maximum rotational speed and the actual rotational speed according to the invention the gradient will be reduced in order not to exceed the maximum rotational speed . here , the reduction of the gradient can take place when dropping below a pre - set threshold value for the difference between the maximum rotational speed and the actual rotational speed . the maximum rotational speed curve running parallel to the v axis has been designated with l . when a gas pedal value dependent maximum speed is exceeded or the gas pedal released , it is possible to leave the acceleration mode and return to the target rotational speed of the standard driving mode after the shift . this is shown in fig5 , wherein the gas pedal value dependent maximum speed has been marked with k . according to the invention , the rotational speed offset between the operating point with or without the acceleration mode is established in such way that , when a renewed downshift demand is recognized during the acceleration mode , the offset will be maintained or slightly reduced so that the downshift corresponding to the driver &# 39 ; s desire can be represented . this is clarified in fig6 . during the earlier described acceleration phase after the first downshift , the gas pedal value is again increased and a new downshift or , as the case may be , downward adjustment is demanded according to the invention . the offset j between the operating point of the demand for the renewed downshift , with or without the acceleration mode , will be somewhat maintained during the subsequent rotational speed change , wherein , when the downshift is completed , the course of the rotational speed according to the rotational speed gradient will be continued according to the invention . the concept according to the invention can also analogously be used for up - shifts , which may be demanded , for example , by the reduction of the gas pedal value . here , after the up - shift or , as the case may be , upward adjustment of the variable speed gear driving continues with a calibrated rotational speed gradient , which deviates accordingly from the flat course in a standard driving program . c course of the rotational speed during a downshift at low speed d course of the rotational speed during a downshift at high speed e course of the gas pedal value during a downshift at low speed f course of the gas pedal value during a downshift at high speed g flat rotational speed course g as a function of the speed without acceleration mode j offset between the operating point of the demand of a renewed downshift with and without acceleration mode