a method for isomerizing isobutene or n - butene to produce a mixture of isobutene and normal butene , and polymerizing at least a portion thereof to produce isobutene / n - butene codimer , which comprieses feeding at least 80 weight % of either the isobutene or n - butene to a catalytic distillation reactor containing a fixed bed acidic cation exchange resin catalyst packing which provides both the catalyst sites and distillation sites for the reaction products , isomerizing a portion of the isobutene or n - butene to produce a mixture of isobutene and n - butene and reacting at least a portion of the isobutene and n - butene to form codimer of isobutene and n - butene , whereby an overhead fraction containing any unreacted isobutene and n - butene and a bottoms fraction containing codimer is produced . the result of the reaction is substantially the same regardless whether the feed is isobutene or n - butene . other aspects of the invention , include combinations of procedures to produce high purity isobutene and n - butene . either isobutene or n - butene product can be recycled as feed , thus substantially carrying out the isomerization to extinction and total conversion to the desired product .