In this paper general classes of stochastic systems described by stochastic integrals of the Volterra type are considered. Existence and uniqueness of random solutions as well as stochastic stability criteria of the Popov frequency form are established. These frequency stability criteria relate not only to the linear system dynamics (or the kernel of the Volterra integral) of the system, but also to the characteristics of the additive and multiplicative random processes that govern the system.