Radical copolymerization of N-methylmaleimide (MeMI) as well as other N-alkylmaleimides (RMI) and isobutene (IB) was carried out with 2,2’-azobis(isobutyronitrile) as an initiator at 60 degrees C. The initial rate of the copolymerization (R(p)) was dependent on the monomer composition and was maximum at the 40 mol % of MeMI in the feed. A solvent effect on the R,and the monomer reactivity ratio was observed in this copolymerization system, i.e., copolymerization in chloroform produced a higher R,and an alternating tendency compared with those in dioxane (r(MeMI) = 0.14, r(IB) = 0 in chloroform and r(MeMI) = 0.47, r(IB) = 0 in dioxane). The alternating copolymer of RMI and IB shows a high glass transition temperature (T-g) and excellent thermal stability, e.g., the T-g and the thermal decomposition temperature (T-d) were 152 and 363 degrees C, respectively, for the alternating copolymer of MeMI and IB. Both the T-g and T-d increased as the concentration of the MeMI unit in the copolymers increased. Colorless transparent sheets were obtained from press molding the alternating copolymers. They showed excellent mechanical and optical properties.