As this paper shows, the magnetic coupling of the inductances of two hysteresis-controlled single-phase AC-to-DC boost power converters connected in parallel leads in connection with a delayed switching of the power transistors to a self-adjusting staggered switching of the partial systems. Thereby, a significant reduction of the ripple of the resulting mains current as compared to the uncoupled case is obtained. Based on the analytical description of the current shapes within a pulse period the dependency on the circuit parameters of the occurring phase displacement of the switching functions of the partial systems is calculated. Furthermore, the effect of an unsymmetry of the power converters on the system behavior is analyzed and the automatic adjustment of the phase shift within a mains period is investigated by digital simulation. The theoretical considerations are verified by measurements on a laboratory model. Finally, the possibility of a substitution of the magnetic coupling of the input inductances of the partial systems by a coupling of the current controls of the power converters is discussed.