Envelope statistics are being frequently used to describe stochastic processes when a more detailed description is either unobtainable or impractical. The response of a nonlinear oscillator subject to nonstationary stochastic excitations is described. This is accomplished by analytically computing the transition probability density of a one‐dimensional Markov process, which approximates the amplitude envelope of the response. For this purpose, an appropriate variation of the solution to the corresponding linear problem is employed. The probability density at various times as well as the mean‐square and standard deviation of the amplitude envelope are computed for specific nonlinearly damped oscillators subject to separable and nonseparable nonstationary excitations. The analytical results are compared with those obtained by a Monte Carlo simulation study. The agreement between the two supports the applicability of the method to a broad class of oscillators.