In this paper, a specific neural network based model for the identification of non-linear systems is proposed. This neural network structure is able to identify a state space non-linear model of the plant. The use of the state space representation presents several advantages that must be taken into account. One of the most important advantages is that the resulting neural model can be easily linearized around different operating points, allowing application of classical stability theorems from the linear systems domain to this class of neural networks. In this way, some useful theoretical results for neural modelling and identification have been obtained and presented in the paper. In this paper, several stability theorems and practical implementation issues are addressed. Examples are also presented which show the training capability of the neural network and the validity of the theory presented.