A novel multilayer discrete-time neural net paradigm is presented for the identification of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms. The NN identifier includes modified delta rule weight tuning and exhibits a learning-while-functioning feature instead of learning-then-functioning, so that the identification is on-line with no explicit off-line learning phase needed. The structure of the neural net (NN) identifier is derived using a passivity aproach. Linearity in the parameters is not required and certainty equivalence is not used. The notion of persistency of excitation (PE) and passivity properties of the multilayer NN are defined and used in the convergence analysis of both the identification error and the weight estimates.