In this paper, the problem of nonlinear random parametric oscillations of a vibration-protected mechanical system is considered. Nonlinear ambiguous functions characterizing the dissipative properties of materials of elastic damping elements of a mechanical system and a dynamic absorber are taken into account using the method of statistical linearization in linear form. Using the Ito method, an analytical expression for the mean square values ​​of the vibration-protected system is obtained.