The present invention relates to a) a catalytic composite comprising a support structure and a catalytic species that is deposited on the support structure, b) a process for the selective oligomerization of lower alkenes and mixtures of alkenes, which process comprises contacting the lower alkenes with the catalytic composite in a catalytic distillation apparatus and under catalytic distillation conditions, and c) a process for producing high octane products, which process comprises hydrogenating one or more catalytic distillation apparatus and under catalytic distillation conditions.