Combinations of dialkylaluminum chlorides and dialkylmagnesium compounds, when used at molar [AlR2Cl]:[MgR2] ratios >= 2, act as universal cocatalysts for all three presently known types of alkene polymerization catalysts-Ziegler-Natta, metallocene, and post-metallocene. When these cocatalysts are used with supported Ti-based Ziegler-Natta catalysts, they produce catalyst systems which are 1.5-2 times more active than the systems utilizing AlR3 compounds as cocatalysts. Combinations of AlR2Cl/MgR2 cocatalysts and various metallocene complexes produce single-center catalyst systems similar to those formed in the presence of MAO. The same cocatalysts activate numerous post-metallocene Ti complexes containing bidentate ligands of a different nature and produce multicenter systems of very high activity. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3271-3285, 2009