A partially crosslinked polymer composition comprisinga) a polymer comprising from 25 to 95% by weight of polypropylene and from 5 to 75% by weight of a propylene copolymer with copolymerized C.sub.2 -C.sub.10 -alk-1-enes, the comonomer content being from 1 to 45% by weight, based on the total polymer,b) a random ethylene copolymer containing from 5 to 20% by weight of copolymerized C.sub.3 -C.sub.10 -alk-1-enes and having a density at room temperature of from 0.89 to 0.925 g/cm.sup.3, andc) an organosilane compound of the formula (I)A.sub.4-n SiR.sub.n (I) where A are identical or different acrylates or methacrylates or vinyl groups, R are identical or different C.sub.1 -C.sub.8 -alkoxy or C.sub.1 -C.sub.8 -acetoxy groups, and n is 1, 2 or 3,can be obtained by reacting a polymer mixture of the polymer a) and the random ethylene copolymer b) with the organosilane compound c) in the presence of a free-radical initiator and in the presence of a condensation catalyst at from 180.degree. to 280.degree. C., at from 1 to 100 bar and at a mean residence time of the reaction mixture of from 0.2 to 10 minutes.