A partially cross-linked polymer composition obtainable by dynamically heat-treating: 95 to 50% by weight of a resin (A) comprising an ethylene copolymer containing 5 to 48% by weight of units derived from at least one monomer selected from vinyl acetate, (meth)acrylic acid, (meth)acrylate ester, glycidyl (meth)acrylate and carbon monoxide, and 5 to 50% by weight of a resin (B) having a melt viscosity (JAI 7-1991) at 180° C. of over 10,000 mPa·Es and comprising a two or more-component propylene copolymer containing 0.1 to 20% by mol of units derived from α-olefins other than propylene, or a blend of the two or more-component propylene copolymer and a propylene homopolymer in the presence of an organic peroxide (C) in an amount of from 0.001 to 4 parts by weight based on 100 parts by weight of the total amount of the resins (A) and (B). A process for producing the polymer compositions is also provided.