Adaptive control has achieved a celebrated success in both theory and application due to its toleration of significant uncertainties in plants. So far, the control of linear systems with time-invariant unknown parameters has been well understood, however, it used to be a difficult topic which took researchers almost two decades to make a breakthrough.  Among all the unsolved fundamental problems at that time, the convergence of the least-squares (LS) based self-tuning regulator (STR) is an important one deserving special mention in adaptive control theory. The idea of the STR is owned to R. E. Kalman, but its rigorous analysis was initiated in 1973 by K. J. Åuström, who brought the LS-STR open problem to the attention of the theoretical world of control. It was not until 1995 that this problem was solved completely. Now, our question is if the system is nonlinear, is the STR still effective? This talk is aimed at the identification and control of nonlinear parameterized systems and trying to answer the STR problem with high degree of nonlinearities in models.