The problem of time domain scattering by a bounded obstacle involves finding the solution of an integral equation, the kernel being a linear operator on the unknown function. This function may be scalar or vector valued, depending on the type of problem; the spatial integration domain may be the boundary of the obstacle or its interior. The stability and convergence of time marching methods for solving transient scattering problems are considered. Conditions are presented which ensure that the discretization errors can be made arbitrary small on any finite time interval for two and three dimensional problems.