Cross-linkable, olefinic polymers synthesized from mixtures of olefinic polymers and ethylenically unsaturated organosilane compounds, which can be grafted, by a 2-step method using thermally decomposing free radical-forming agents by heating the mixtures to a temperature of 30.degree. to 110.degree. C. below the softening temperature or the crystallite melting point of the olefinic polymers used and subsequently heating the mixtures to a reaction temperature of 10.degree. to 60 .degree. C. below the softening temperature or the crystallite melting point of the olefinic polymers used. In the alternative, they can be grafted by a method involving the action of ionizing radiation with simultaneous absorption of organosilane compounds and the action of radiation. The method is suitable for producing films, sheets, fibers, panels, coatings, pipes, hollow objects, foamed materials and molded articles.