A new method for simulating cyclically switching systems (power electronics circuits) is presented. Partial results of this paper were reported at I.E.E.E. Power Electronics Specialists Conference (PESC ‘89), Milwaukee. The starting idea is the application of a familiar tool for engineers: the Laplace transform for studying such systems, whose basic cell is an electronic converter. The switching elements of the converter are extracted in a two-port (alternor), which is defined in order to simulate the possible cyclically circuit operation both in continuous and discontinuous conduction mode. The remaining part of the circuit is linear time-invariant; its nodal equations are formulated. By adding the generalized alternor equations, an s-domain system of equations is obtained. This describes the global dynamic behaviour of the converter. The s-domain solution is computed and its inverse Laplace transform is found. The transient and steady-state responses, computed in such a way, mirror exactly the converter waveforms. All the steps of the algorithm can be implemented in a computer program that makes use of a symbolic computer package, such as MACSYMA. The method, suitable for the simulation of any cyclically switching system, is exemplified here by the analysis of a DC-to-DC buck-boost converter.