We consider the response spectrum of a dynamical system described byLr(t)+εN[r,ṙ,r̈⋯]=f(t), for whichLis a linear differential operator in time,Nis a nonlinear analytic function of the responser(t) and its derivatives, andf(t) is a Gaussian random process with a given power spectrum. A perturbation technique is applied, which yields the spectral density of the response in a series in powers of the coupling constant ε. The methods is, therefore, applicable only if the system remains stable in the range of ε. Some general properties of the expansion are presented, and a sample calculation of a perturbed spectrum is outlined. The method is applicable to such problems as Brownian motion with nonlinear viscous forces and the coupling of energy from a nonlinear mode into other modes in a complex structure.