In this work, the spectral density of the following multi-DOF nonlinear damping model is investigated : Mx + D(o)x + gammaD(x, x) + Kx = sigman(t) where gamma > 0 is a small parameter. A formula for the spectral density is established with O(gamma2) accuracy based upon the Fokker-Planck technique and perturbation. One of the features of the multi-DOF osculation system is that x and x are generally correlated in stationary state. This is true even for linear systems. Necessary and sufficient conditions for uncorrelatedness are given for linear systems. Since the first-order statistics R(xx)(0) and R(xy)(0), where gamma = x, appear in the spectral density formula it is desirable to have the explicit stationary probability density for the purpose of evaluating R(xx)(0) and R(xy)(0). However, in general, as in the single DOF case, an expression for the stationary density is not available. This note gives the explicit stationary density of an "energy"-type nonlinear damping model Mx + mu(E(D))Dx + Kx = sigman(t) in which the "energy" E(D) is defined as E(D) = 112(x(T)KDx + y(T)M Dy) where D > 0 is assumed to commmute with K and M. In the end, an energy-type nonlinear damping model is worked out completely as an illustration.