To identify on-line a quite general class of non-linear systems, this paper proposes a new stable learning law of the multilayer dynamic neural networks. A Lyapunov-like analysis is used to derive this stable learning procedure for the hidden layer as well as for the output layer. An algebraic Riccati equation is considered to construct a bound for the identification error. The suggested learning algorithm is similar to the well-known backpropagation rule of the multilayer perceptrons but with an additional term which assure the stability property of the identification error.