The probability density Junction of the responses of nonlinear random vibration of a multi-degree-of-freedom system is formulated in the defined domain as an exponentialfunction of polynomials in state variables. The probability density function is assumed tobe governed by Fokker-Planck-Kolmogorov (FPK) equation. Special measure is taken to satisfy the FPK equation in the average sense of integration with the assumed functionand quadratic algebraic equations are obtained for determining the unknown probabilitydensity function. Two-degree-of-freedom systems are analyzed with the proposed methodto validate the method for nonlinear multi-degree-of-freedom systems. The probabilitydensity functions obtained with the proposed method are compared with the obtainable exact and simulated ones. Numerical results showed that the probability density functionsolutions obtained with the presented method are much closer to the exact and simulatedsolutions even for highly nonlinear systems with both external and parametric excitations. © 2000 ASME.