The paper presents an approach to the Model Reference Adaptive Control (MRAC) design for nonlinear dynamical systems. A nonlinear reference system is considered such that its response is designed to be stable via Successive Approximation Approach (SAA). Having designed the stable reference model through the SAA, MRAC is then formulated for nonlinear plant dynamics with a new adaptation rule to guarantee the convergence of the nonlinear plant response to that of the response of the nonlinear reference model. The proposed design methodology is illustrated with examples for different case studies.