The inventive copolymer composition is satisfactorily curable or vulcanizable into, for example, a rubbery elastomer even by an organic peroxide contained therein as a crosslinking agent. The crosslinkable copolymer comprised therein is a polymer having, in a molecule, at least two monomeric units each having a vinyl-containing organosilicon pendant group represented by the general formula (Vi.sub.m R.sup.1.sub.n SiO).sub.a Vi.sub.b R.sup.2.sub.c Si--, in which Vi is a vinyl group, R.sup.1 is a hydrogen atom or a group selected from the class consisting of monovalent hydrocarbon groups free from aliphatic unsaturation, hydroxy group and hydrolyzable groups excepting halogen atoms, R.sup.2 is a hydrogen atom or a monovalent hydrocarbon group, m is 1, 2 or 3, n is zero, 1 or 2, a is 1, 2 or 3, b is zero, 1 or 2 and c is zero, 1 or 2 with the proviso that a+b=1, 2 or 3 and a+b+c=3. Such a copolymer can be prepared by the copolymerization of a first ordinary ethylenically unsaturated monomer and a second monomer having, simultaneously in a molecule, an ethylenically unsaturated linkage copolymerizable with the first monomer and the vinyl-containing organosilicon group of the above given formula.