The paper considers the development of a new type of artificial neural network and its applicability to non-linear system identification. This is the functional-link neural network with internal dynamic elements. The net consists of a single layer where the non-linearity is firstly introduced by enhancing the input pattern with a functional expansion. The internal dynamic elements are auto-regressive moving average filters that implement local activation feedback and local output feedback, respectively. Experimental results demonstrate a better capability of generalisation of the suggested neural network in comparison with the functional-link net with static structure and external dynamic elements, used so far to perform system identification.