This work provides a framework for the approximation of a dynamic system of the form x = f(x) + g(x)u by Dynamic Recurrent Neural Network (DRNNs). This extends previous work in which approximate realization of autonomous dynamic systems were proven. Given certain conditions, the first p output neural units of a dynamic n-dimensional neural model approximate at a desired proximity a p-dimensional dynamic system with n > p. The neural architecture studied is then successfully implemented in a nonlinear multivariable system identification study case.