The radiation-induced solid-state polymerization in the binary systems such as acryl-amide–methacrylamide and acrylamide–acenaphthylene was studied. The former system forms a solid solution, and the latter one forms a eutectic mixture. In the solid solution, the polymerization proceeds homogeneously and copolymer is formed, while in the eutectic mixture, it proceeds heterogeneously, forming only homopolymer. The post-polymerization of the same binary systems was also studied. Linearity between the conversion and the logarithm of the post-polymerization time was found for the various monomer compositions at various temperatures. This relationship satisfied the kinetic equation presented by Morawetz et al. for the post-polymerization of acrylamide. The kinetics of the binary systems might be considered similarly to the single system, considering that the crystalline state of the system is changed by the monomer compositions.