This paper is concerned with the stability, in a stochastic sense, of circuits or systems described by ordinary differential equations with randomly time varying parameters. Sufficient conditions for stability in the mean square are obtained by an extension of “Lyapunov's Second Method” to stochastic problems. The general result while applicable to non-linear as well as linear systems, presents formidable computational difficulties except for a few special cases which are tabulated. The linear case with certain assumptions concerning the statistical independence of parameter variation is carried out. © 1959, IEEE. All rights reserved.