Linear alternating copolymers of carbon monoxide and at least one compound containing an alkenyl unsaturation are obtained by reaction between carbon monoxide and at least one compound containing an alkenyl unsaturation, in a solvent which is liquid under the operating conditions, in the presence of a preformed bischelated catalyst having general formula (I) active without cocatalysts: �Pd(chel)(chel')!.sup.++ �A.sup.- !.sub.2 (I) wherein: chel and chel', the same or different, represent a nitrogenated or phosphorated bidentate chelating agent, and A.sup.- represents an essentially non-co-ordinating, non-esterifiable and non-labile anion selected from (3,5-(CF.sub.3).sub.2 -C.sub.6 H.sub.3).sub.4 B.sup.-, tetra(perfluorophenyl)borate B(C.sub.6 F.sub.5).sub.4.sup.- and Al(C.sub.6 F.sub.5).sub.4.sup.-.