To provide a process for trimerizing (e.g. ethylene into 1-hexene) or oligomerizing an olefin at high selectivity and productivity in the presence of a min. amt. of or in the absence of a solvent.

An olefin is oligomerized by bringing it into contact with an olefin oligomerization catalyst system in a solvent. The catalyst system contains a chromium source, a pyrrole compd., and an alkylmetal and optionally contains a halide source. The solvent corresponds to a product of the oligomerization process. Pref. the chromium source is a chromium (II) compd. or esp. a chromium (III) compd. [e.g. chromium tris (2-ethylhexanoate)]. Examples of the pyrrole compd. are pyrrole and 2,5-dimethylpyrrole. An example of the alkylmetal is a mixture of ethylaluminum dichloride and triethylaluminum.