The paper shows that the response of the random Rayleigh system, which is under harmonic and random excitations, can be found by a system of algebraic equations. The analytical approach is based on the stochastic averaging method and equivalent linearization method in Cartesian coordinates so that the Fokker-Planck equation associated with the linear equations obtained can be solved exactly by the technique of auxiliary function. The harmonic excitation frequency is taken to be in the neighborho