Model epoxy resins with controlled crosslinking densities were prepared from a commercially available DGEBA (Epon Resin 825(R) from Shell Chemical) and alpha,omega-aliphatic diamines having different lengths of the aliphatic chain. The mixtures were always prepared in stoichiometric ratio. Dumbbell specimens, either with a cylindrical (with thin walls) or a rectangular cross section, have been subjected to combined static tensile strains (applied vertically) and dynamic torsional strains (applied horizontally). The experiments were performed at temperatures encompassing the glassy and the rubbery range of each investigated resin. The apparatus, by which the combined dynamic and static stresses were applied, was equipped with load cells for measurement of stresses developed in the specimens, both in tension and in shear. In this paper, results concerning the effect of the above combinations of stresses on stress relaxation rates in tension are shown. The main conclusion of this study is that combinations of dynamic and static stresses affect the network chain mobility, as it is expressed by the stress relaxation rate, in a way depending on temperature and frequency of torsional oscillations, as well as the crosslinking density of the polymer. For the most flexible epoxy resins investigated in this work, the superimposed stressing experiments led to a stiffening of the structure in the glassy state, while an opposite effect has been observed for the most rigid resins in similar conditions. It seems that the behavior of the investigated epoxy resins in complex fields of stresses is governed by a balance between two competitive processes: free volume increase (by a strain-induced dilatation mechanism), and physical aging and short range orientation.