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In this paper, a new multi-layer neural network (MNN) based system identification scheme in discrete-time is proposed for a general class of nonlinear discrete-time systems with guaranteed asymptotic convergence of the identification error. Then, a MNN based direct adaptive MNN controller design is introduced for a different class of nonlinear discrete-time systems. The unique aspect of the proposed method is the asymptotic stability assurances of the system identification and tracking errors in the presence of MNN reconstruction errors by using an auxiliary robust term which is a function of the outer-layer NN weights. Finally, simulation examples are presented to illustrate the MNN based estimation and control scheme.