We present the results of computer simulations of model polymer networks containing stiff and roughly spherical colloidal particles at 20% volume fraction. We employ the coarse-grained "dissipative particle dynamics" model (DPD). The filler particles may be either well dispersed or aggregated, and the strength of their interaction can be tuned by changing the parameters of the polymer-filler nonbonded potentials. By performing nonequilibrium molecular dynamics simulations, we are able to probe directly the viscoelastic behavior of the composites under oscillatory shear deformations of variable amplitude and frequency. The strength of the particle-particle interactions and sample morphology has a certain effect on the small-strain moduli. In some cases, we also observe a nonlinear viscoelastic behavior as a function of increasing shear amplitude. However, the characteristics of this nonlinearity are different from the experimentally observed "Payne effect". Therefore, the origin of this effect does not seem to be entirely and directly related to particle-particle interactions, as is frequently assumed.