Abstract: Introduces n-mode generalized center-of-mass coordinetes corresponding respectively to each dominant mode of the system derived form a n degree-of-fredom nolilinear vibrational system.The problem of solving a set of differential equations of n generalized coordinates is thus reduced to that of solving n differntial equations having single degree of freedom of vibration for each mode of generalized center of mass coordinathes.The asymptotic solution of each of the genelized coordinates can be obtained by the development of multiplex Fourier series and solving a set of linear algebraic equations.An analysis on the single frequency vibration of multi-degree-offreedom nolilinear vibrational system is given and can be taken as a special case.