In spite of large-scale investigations of homogeneous single-site metallocene catalysts and systems based on them, the problem of controlling their activity, chemo- and stereoselectivity with the aim of developing efficient methods for the preparation of practically useful products of alkenes transformation, such as dimers, oligomers, and polymers, still remains topical. Here we studied catalytic activity of differently structured zirconocenes (10 examples of cyclopentadienyl and indenyl complexes) and co-catalysts activating the system, namely HAlBui2, MMAO-12 or (Ph3C)[B(C6F5)4] at low activator/Zr ratios in 1-hexene oligomerization reaction. The influence of catalyst structure and system composition on alkene conversion, type of products formed and reaction stereoselectivity was investigated. The composition of hydride intermediates forming in the systems L2ZrCl2 (L2= ansa-Me2CCp2)-HAlBui2-activator was studied by NMR and the participation of biszirconium hydride complex as the precursor of catalytically active sites of the alkene dimerization reaction was shown.