Abstract: In this paper,an asymptotic method is presented for the analysis of a class ofstrongly nonlinear autonomous vibrating systems with many degrees of freedom。It can beviwed as a generalization of the new asymptotic method￣1.This method is suitable for thesystems in which primary resonance may occur。Using the present method the equationsgoverning the amplitudes and the phase factors are established.Two numerical examplesare presented which served to demonstrate the effectiveness of the present method。