ABSTRACT
The problem of the stability of systems, parameters of which are random processes, is very important for different fields of science and engineering, and particularly - of mechanics. The present paper is devoted to the investigation of the stability of the zero solution for linear integrodifferential equations, describing the behavior of viscoelastic distributed parameter systems under an action of parametric loads, which are assumed in the form of random ergodic stationary processes. The conditions of the asymptotic almost sure stability and stability in the mean square are obtained, if the relaxation kernel of the material has an enough arbitrary difference form.
