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Users of nonlinear transient network-analysis programs, which use explicit integration procedures, have reported that excessive computer time is required to compute the transient response of networks containing widely separated time constants. Several recent papers have shown that for these problems significant computation-time reductions can be obtained by using implicit integration formulas. This paper is concerned with the selection and implementation of an implicit integration formula used in the CIRPAC nonlinear transient network-analysis program. Time-comparison data presented here indicate that the integration system that is described in this paper is significantly faster than the integration system of a network-analysis program that uses an explicit integration algorithm.