<p>The invention concerns a process for the production of copolymers of propylene and but-1-ene which can be used for the production of hollow bodies or heat-sealable films and wherein the proportion by weight of units derived from but-1-ene is from 10 to 40% and wherein the proportion of isolated ethyl branches is at least equal to the square of the proportion of units derived from propylene contained in said polymers. The process is characterized in that a gaseous mixture of propylene and but-1-ene is brought into contact, in the absence of liquid diluent, with a catalytic system which is stereospecific in the polymerization of propylene alone.</p>
