Summary: The semidiscretization in space of Volterra-Fredholm integral equations (arising for example, as mathematical models of the spreading of epidemics) leads to large systems of Volterra integral equations. Here, we study inexpensive time-stepping methods using certain direct quadrature methods which are employed in a way that exploits the local superconvergence properties of spatial collocation. The performance of these methods is then compared with that of time-stepping based on collocation methods.