Copolymers of 4-methylpentene-1 are prepared by copolymerization of 4-methylpentene-1 with one or more other C.sub.2-18 .alpha.-alkenes at a temperature above room temperature and in the presence of hydrogen using a Ziegler/Natta catalyst system. The polymerization is carried out at a relatively very high temperature and in the presence of an inert gas with the proviso that the partial pressures of the inert gas and of the hydrogen and the sum of the partial pressures of the inert gas, hydrogen and 4-methylpentene-1 have specific values. In this way, copolymers having large crystalline fractions are obtained in a high yield per unit of catalyst system per unit time.