Abstract: Hyperstability theory is a significant tool for stability proofs of adaptive control, but so far it is only used for deterministic systems. Based on a further study of hypestability theory and a suitable conversion of the adaptive control construction, hyperstability theory are used for the stability proofs of stochastic adaptive control. It is shown that hyperstability theory can be used in stochastic case and has advantages over the previous Martingale function method and Ljung's ODE method. Comparing with the Martingale method, it does not require to build sedulously a stochastic Lyapunov function, which is usually very difficult to do. And it also omits the condition of stationary process of system noise, which is necessary in Ljung's ODE method.