Most predictive control algorithms, including the generalized predictive control (GPC) (Clarke et al., 1987), are based on linear dynamics. Many processes are severely nonlinear and would require high-order linear approximations. Another approach, which is presented here, is to extend the basic adaptive GPC algorithm to a nonlinear form. This provides a nonlinear predictive controller which is shown to be very effective in the control of processes with nonlinearities that can be suitably modeled using general Volterra, Hammerstein, and bilinear models. In developing this algorithm, the process dynamics are not restricted to a particular order, as is the case with the current nonlinear adaptive algorithms. Simulations are presented using a number of examples, and the steady state properties are discussed.