Thermally stable copolymers with an alternating repeating structure, poly(RMI‐alt‐IB)s, were synthesized by radical copolymerization of N‐substituted maleimides containing a polar group with isobutene. The onset temperature of decomposition was higher than 300 °C and the glass‐transition temperature increased by the introduction of hydroxy and carboxy groups. IR spectroscopic analysis revealed the role of intermolecular hydrogen bonding on the thermal stability of the copolymers. It was also revealed that the amount of water absorbed into poly(RMI‐alt‐IB)s with a hydroxymethyl substituent was as high as 270% of the weight of the used polymer, while the introduction of a carboxy group resulted in lower water absorption properties.