Provided are catalyst components which enable the production of industrially useful copolymers which are composed of an alpha-olefin and a (meth)acrylic monomer or of two kinds of alpha-olefins and a (meth)acrylic monomer and which have each a high molecular weight and a high comonomer content. Also provided is a process for production of the copolymers using the same. A copolymer of an alpha-olefin and a (meth)acrylic monomer is produced using a catalyst composition containing a metal complex wherein a metal is complexed with a ligand represented by general formula (1). In general formula (1), Y is phosphorus or arsenic; Z is -SO3H or -CO2H; and at least one of R1 to R4 is a substituent wherein the carbon atom directly attached to the aromatic ring is bonded by single bonds to two or more atoms selected from a group consisting of C, O and N.