In this paper, we propose a recursive identification technique for nonlinear discrete-time multivariable dynamical systems. Extending an early result to multivariable systems , the technique approaches a nonlinear system identification problem in two stages: One is to build up recursively a RBF (Radial-Basis-Function) neural net model structure including the size of the neural net and the parameters in the RBF neurons; the other is to design a stable recursive weight updating algorithm to obtain the weights of the net in an efficient way. Heuristics are employed to analyze the effect of RBF net parameters to the error of identification, leading to a simple but effective means to establish these parameters. The weight updating algorithm is developed based on ideas in the theory of adaptive control. Key stability results are proved in the paper along with illustrative examples to show the effectiveness of applying such a technique and other practical considerations.