The influence of the nature of a cocatalyst, a stabilizing ligand, and an introduced modifier on the behavior of the ethylene oligo- and polymerization reaction in the presence of the Cr(acac)(3)-AlR3-L-M catalyst system, where AlR3 is triethylaluminum (AlEt3), dichloroethylaluminum (AlEtCl2), or methylalumoxane (MAO); L is pyrrole (PyH) or bis(diphenylphosphino)cyclohexylamine ((Ph2P)(2)NCy); and M is tetrachloromethane (CCl4), has been studied. The maximal selectivity for hexene-1 has been found to be 86 wt %.