Finding an appropriatetrade-off between performanceand computational complexity is an important issue in the design of adaptive algorithms. This paper introduces an algorithm for adaptive identification of Non-linear Auto-Regressive with eXogenous inputs (NARX) models of a nonlinear system. This algorithm, which is derived from the Matching Pursuit algorithm, is used for the online identification of nonlinear dynamic systems. The NARX model is expanded into a sum of non-orthogonal spline basis functions. The convergence of the algorithm is proved for certain signal assumptions. Simulation experiments are provided for examples previously solved in the literature.