Novel maleimide copolymers have at least two monomeric units, a maleimide unit and a vinyl unit having a pendant group, the pendant group having two to twenty-one carbon atoms, at least one nitrogen atom and at least one oxygen atom. The copolymer has an average molecular weight between about 1,000 and about 6,000,000. Preferred maleimide copolymers include acrylamide/maleimide copolymers, N-vinyl amide/maleimide copolymers, vinyl lactam/maleimide copolymers, alkenyl cyclic imino ether/maleimide copolymers, and acryloylamide/maleimide copolymers. The substantially water soluble maleimide copolymers are useful for inhibiting the formation of clathrate hydrates in a fluid having hydrate-forming constituents by reducing the rate of nucleation, growth, and/or agglomeration of gas hydrate crystals in a petroleum fluid stream, thereby inhibiting the formation of a hydrate blockage in the pipe conveying the petroleum fluid stream. The inhibitor can be used conveniently at low concentrations, for example in the range of from about 0.01% to about 5% by weight of the water present in the oil or gas stream, to effectively treat a petroleum fluid having a water phase.