The paper is concerned with the study of stability in the quadratic mean of dynamical systems described by Ito stochastic differential equations. In the first part of the paper, by using vector positive functions, conditions of asymptotic and exponential stability in the quadratic mean are developed. In the second part of the paper a comparison principle which reduces the stability analysis problem of stochastic dynamical systems to an analogous problem for a one-dimensional deterministic system is established.