The use of novel heterogeneous catalyst complexes as catalysts for oligomerizing alpha-olefins is disclosed. The complexes are formed from (i) a solid olefin polymer having a linear backbone and a plurality of pendant omega-hydroxyalkyl groups, (ii) an organomagnesium halide, and (iii) a boron trihalide, preferably BF.sub.3. The complexes can be recovered and reused repeatedly in batch-type operations and can be used for long periods of time in continuous or semi-continuous operations without replenishment of their boron trifluoride content.