The main aim of this research activity is that of developing constitutive equations for the rheology of macromolecular fluids. In particular, we are interested in entangled macromolecular fluids. In spite of the complex rheological behavior of these fluids, the constitutive equations should be simple enough to be used in algorithms for complex flow simulations. In order to better describe the nonlinear rheological behaviour of these materials analytical models are sometimes replaced by simulation models explicitly accounting for the many-chain nature of the entangled polymer dynamics. More specifically we resort to Brownian dynamics methods as well as to non-equilibrium molecular dynamics.