The level crossing problem is discussed for a multi-dimentional nonlinear system subjected to an amplitude modulated nonwhite random excitation. The first passage probability and the probability distribution of the level crossings are approximately represented by a few low order factorial moments of crossings, which are calculated by using the equivalent linearization technique and assuming the Gaussian probability distribution of the response process. The dependence of occurrence of the level crossing upon the number of events is taken into consideration. Numerical results are compared with the corresponding digital simulation results for a single degree of freedom system with bilinear hysteresis excited by noise with an exponentially decaying harmonic correlation function.