A design procedure for adaptive cascade control of a class of uncertain single-input nonlinear systems in strict feedback form is proposed. The control scheme is based on a backstepping design endowed with a modeling error estimator. In the one-dimensional case, the resulting controller is equivalent to a PI control law. Constructed as an extension of the one-dimensional case, the high-dimensional case can be interpreted as a cascade PI controllers. Stability of the underlying closed-loop system is established from results of singularly perturbed nonlinear systems. Our results are illustrated via numerical simulations.