Since incompatibility of two homopolymers is the rule, it was of interest to see if mixing a corresponding copolymer (graft, block, or random) with a mixture of two incompatible homopolymers would bring about compatibility. For this study we limited ourselves to two systems of atactic polymers: polystyrene/poly (methyl methacrylate), and polystyrene/cis-l,4-polyisoprene since, in these systems, no crystallization occurs at normal temperatures. Investigation of these systems in the solid state—i.e., as films, prepared from polymer solutions by evaporation, enabled us to establish compatibility limits with considerable accuracy. The most important parameters for compatibility of homopolymer-copolymer mixtures seem to be, among other things: composition, molecular weight, and structure of the copolymers. Ternary diagrams for a mixture of two homopolymers and a copolymer show quite plainly that only block copolymers induce a certain compatibility. This is especially true when the polymer proportion in the block copolymers is approximately 50/50, and molecular weight of the homopolymers is substantially lower than that of the copolymer. Graft and random copolymers have little or no effect at all, upon compatibility. We also examined the relation between compatibility and impact strength for the system: polystyrene/polyisoprene/block copolymer.