High activity and selectivity of the samples of ASM amorphous mesoporous aluminosilicates in the synthesis of practically important oligomers of various unsaturated compounds (C-5-C-16 linear alpha-olefins, cyclooctene, norbornene, and alpha-methylstyrene) is found. The oligomerization products obtained in the presence of ASM have a broader molecular weight distribution in comparison with the oligomers synthesized over the H-Beta zeolite. The mesoporous structure of the ASM aluminosilicate provides the preparation of dimers of cyclooctene with high selectivity without cycle opening.