The response of a nonlinear oscillator excited by white noise is considered. A truncated series of Hermite polynomials is used as an approximation to the probability density function. This series and the associated Fokker‐Planck equation are used to generate two sets of coupled differential equations for time‐dependent moments. The first set is for moments of variables evaluated at the same time; the solution yields, for example, the nonstationary mean‐square value. The second set is for moments of variables evaluated at two different times. This second set uses the solution of the first set as initial conditions. A single‐sided Fourier transform of the second set yields coupled complex algebraic equations that can be solved numerically for the spectrum. Examples are shown of spectra for the Duffing oscillator showing an increase in effective resonance frequency and broadening of the peak as the excitation level is increased, and for the van der Pol oscillator showing an entrained limit cycle response at low excitation level that disappears as the excitation level is increased. [Work supported by NSERC.]