An adaptive law for multi-input multi-output discrete polynomic non-linear systems, which can be used for both control and identification is investigated by using the Lyapunov method. It has a simple structure and a convenient form for computation. For control problems, serial-type and parallel-type model-reference adaptive schemes are proposed and a criterion for the selection of the types is given. For identification problems, two conditions for identifiability with respect to input and output data and known constant matrices of the system are derived. To show the effectiveness of this method, a model-reference adaptive scheme for Volterra's prey-predator system is constructed. Digital simulation of the scheme confirms that this method is useful for both control and identification of discrete and continuous systems.