This paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints. In particular, for a Hammerstein nonlinear sampled-data system in which the output sampling period is an integer multiple of the input updating period, we derive, by using a polynomial transformation technique, a mathematical model which is suitable for parameter estimation with dual-rate measurement data. Further, we present an adaptive control scheme for such a dual-rate nonlinear system; the parameter estimation-based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed-loop system is stable and globally convergent. The simulation results are included.