An effective method enhances energy saving at low load in a resonant converter with a hysteretic control scheme for implementing burst-mode at light load. The method causes a current controlled oscillator of the converter to stop oscillating when a feedback control current of the output voltage of the converter reaches a first threshold value, and introduces a nonlinearity in the functional relation between the frequency of oscillation and said feedback control current or in a derivative of the functional relation, while the control current is between a lower, second threshold value and the first threshold value, such that the frequency of oscillation remains equal or smaller than the frequency of oscillation when the control current is equal to the second threshold value. Several circuital implementations are illustrated, all of simple realization without requiring any costly microcontroller.