Based on a certain hypothesis,the strongly nonlinear system was transformed into a weakly nonlinear system by introducing a parameter transformation.Its solutions were expanded into the improved Fourier series,and the resonance cycle solutions were conveniently obtained by the undetermined parameter method.Using the method,we studied the principal resonance cycle solutions of the Duffing equation,the 3 ultraharmonic resonance cycle solutions of the Van der Pol-Mathieu equation.The examples showed that the approximate solutions closely coincided with numerical solutions.