An identification algorithm for time-varying nonlinear systems using a sequential learning scheme with a minimal radial basis function neural network (RBFNN) is presented. The learning algorithm combines the growth criterion of the resource allocating network of Platt with a pruning strategy based on the relative contribution of each hidden unit of the RBFNN to the overall network output. The performance of the algorithm is evaluated on the identification of nonlinear systems with both fixed and time-varying dynamics and also on a static function approximation problem. The nonlinear system with the fixed dynamics have been studied extensively earlier by Chen and Billings and the study with the time-varying dynamics reported is new. For the identification of fixed dynamics case, the resulting RBFNN is shown to be more compact and produces smaller output errors than the hybrid learning algorithm of Chen and Billings. In the case of time-varying dynamics, the algorithm is shown to adjust (add/drop) the hidden neurons of the RBFNN to ’adaptively track’ the dynamics of the nonlinear system with a minimal RBF network.