Both plastic and viscoelastic properties were investigated on neat polymethylmethacrylate (PMMA) and methylmethacrylate-based random copolymers including N-substituted maleimide units. A strong coupling was evidenced between the glass transition motions and the secondary transition motions for PMMA samples rapidly quenched from the molten state. This coupling was shown to diminish markedly in the case of aged PMMA and to disappear almost completely in the case of MMA-maleimide copolymers having a maleimide content as small as 5 mol%. Thus, it strongly suggests that a greater compacity of the glassy PMMA matrix and (or) the presence of stiff maleimide units in the copolymers are sufficient to hinder the early occurrence of large scale conformational motions in the secondary transition region. In addition, it was shown that the strain softening that follows the yield point is also important for aged PMMA and maleimide-rich, copolymers, but tends to vanish in the other samples. Therefore, the probable origin, at least in this series of materials, of the strain softening would be the different nature of the molecular motions that occur in the secondary relaxation region and in the glass transition region.