Abstract: The invention provides a process for the preparation of but-1-ene homopolymers or copolymers of but-1-ene containing up to 15% by weight of at least one other .alpha.-olefin by the stereo-specific polymerization, using a Ziegler-Natta catalyst, of but-1-ene in a homogeneous reaction mixture. By employing a homogeneous reaction mixture comprising at least 70% by weight of but-1-ene and from 1 to 30% by weight of an inert hydrocarbon solvent which is capable of dissolving at least 100 g/l of an isotactic polybutene it is possible to employ reaction temperatures of from 35.degree. to 55.degree. C., thereby improving the quality of the resulting but-1-ene polymer while avoiding precipitation of polymer during the course of the reaction.