The parameter identification of a class of time-varying stochastic systems is considered in this paper. Online schemes which track the time-varying parameters in real time are proposed. Conditions which guarantee either almost sure convergence of the estimation error to the null or bounded mean-square error are obtained. The analysis is based on stochastic Lyapunov functions. This allows the convergence conditions to be weakened, and makes investigation of the stability problem of the proposed identification schemes possible.