In the classical theory of self-tuning regulators,it always requires that the conditional variances of the systems noises are bounded.However,such a requirement may not be satisfied when modeling many practical systems,and one significant example is the well-known ARCH(autoregressive conditional heteroscedasticity)model in econometrics.The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedas-tic noises,where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle.The authors will show that under some natural con-ditions on the system structure and the noises with unbounded conditional variances,the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal.Thus,this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.