The extension of Quadratic Dynamic Matrix Control (QDMC) to nonlinear process models is an attractive option for industrial implementation. Although a nonlinear model is utilized, one has to solve only a single Quadratic Program on-line. In this paper, we present the stability properties for the global asymptotic stability of the closed-loop system under NLQDMC law. The conservativeness of these properties is examined by following the steps of the proofs when this algorithm is applied to a simple example. We also demonstrate the application of the nonlinear version of QDMC to processes for which the sign of the system gain changes around the operating point.