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In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDEs), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compute a new R0-like threshold quantity and an implicit analytical relation between this and the finaldoi:10.1103/physrevlett.115.078701 pmid:26317749 fatcat:lpjn4ly4hngvzd2k6qzzt2ofem