A stochastic model for some class of nonlinear oscillators, which includes a van der Pol-type oscillator with random parameters, is analyzed in the diffusion limit. That is, small random fluctuations and long time are considered, whiIe the nonlinearity is also assumed to be small. We show that there exist stationary distributions, independent of the phase of the oscillator, a result proved earlier by R. L. Stratonovich assuming the random perturbations of the frequency to be delta correlated. The time behavior of the moments of the displacement of the oscillator from its rest position is also investigated and the results are compared with the corresponding ones for the linear random oscillator. A numerical study is also performed for the first two moments and plots are given.