Earthquakes on faults in the brittle upper crust cause sudden changes in pore fluid pressure as well as viscoelastic flow in the lower crust and lithospheric mantle, which affect the postseismic stress and velocity fields in the crust. However, the relative importance of these processes during the postseismic phase has not been systematically studied. In this study, we use 2D finite-element models for intracontinental dip-slip faults to investigate the interaction of pore fluid pressure changes and postseismic viscoelastic relaxation during the earthquake cycle. In different experiments, we vary the permeability of the crust and the viscosity of the lower crust or lithospheric mantle, while keeping the other parameters constant. The results show that the earthquake induced pore pressure changes dissipate within a few days to decades, depending on the permeability of the crust. Therefore, poroelastic effects dominate the velocity field in the first few months, but still affect the velocity field years after the earthquake if the permeability of the upper crust is sufficiently low. Viscoelastic relaxation may also occur in the early postseismic phase for sufficiently low viscosities and then dominates the velocity field from about the second postseismic year onward. Depending on the viscosity, the viscoelastic flow may persist for several decades. Our findings imply that both poroelastic effects and viscoelastic relaxation may overlap earlier and over longer time periods than previously thought, which should be considered when interpreting aftershock distributions, postseismic Coulomb stress changes and surface displacements.