The mechanical relaxation spectrum of poly(monocyclohexylmethylene itaconate) (PMCMI) exhibits two well-developed absorptions in the glassy state that in increasing temperature order are named gamma and beta absorptions. Owing to the restricted conformational versatility of the backbone, the polymer presents a weak glass-rubber relaxation whose intensity is significantly lower than that of the gamma absorption. Comparison of the mechanical spectrum of this polymer with that of poly(dicyclohexylmethylene itaconate) (PDCMI) allows the conclusion that the beta relaxation is produced by motions in which the - COOCH2C6H11 side groups are involved. The location of the mechanical gamma gamma peak suggests that this absorption is produced by flipping conformational transitions in the cyclohexyl residue. Three dielectric absorptions are observed in the glassy state of PMCMI which in increasing temperature order are called delta, gamma, and beta relaxations. Both the location and the activation energy of the dielectric and mechanical beta absorptions suggest that both relaxations are caused by the same molecular motions. Dipolar interactions in the liquid and glassy state are calculated and the results compared with those experimentally evaluated.