Disclosed herein is a high molecular composite material, which comprises as one component thereof a water insolubilized homopolymer of at least one monomer selected from specific N-alkyl- or N-alkylene-substituted (meth)acrylamides, a second copolymer of said at least one monomer with one or more monomers other than the (meth)acrylamides and copolymerizable therewith, or a water-insolubilized product of the homopolymer or either first or second copolymer. The water-insoluble product can form, with a low or high molecular compound containing one or more active hydrogen or hydrophobic groups, a composite material which may be applied widely for absorbing and desorbing a variety of valuable synthetic compounds and natural matter.