Abstract For the integration of partial differential equations, we distinguish explicit and implicit methods. In this paper, we consider an explicit-implicit method, which follows from the truncation of the solution process of a fully implicit method. Such a method is of interest because not only better vectorizing properties can be obtained by increasing the explicit part, but the method also fits well in a domain-decomposition approach. In this paper, we focus on the feasibility of such methods by studying their stability and accuracy properties. Nevertheless, we also did some experiments on vectorcomputers to show that for a sufficient degree of explicitness our method is more efficient than fully implicit methods.