We model dc–dc power converters using the complementarity formalism. For each position of the switches, the dynamics is given by a linear complementarity system which incorporates, in a natural way, the description of generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM can be stated. As an example, this result is used to identify the GDCM for the switch configurations of the Čuk converter. Simulation results, showing a variety of behaviors, such as persistent or re-entering GDCM, are presented.