The paper presents a model reference adaptive control (MRAC) design which maintains stability around the equilibrium of the tracking error in the presence of unmodelled dynamics. Only a slighta prioriknowledge in terms of lower and upper bounds for the absolute values of the parameters and orders of the unmodelled dynamics is required. The key to achieving signal boundedness is to use an additional parameter in the adaptive controller which involves the use of thea prioriknowledge concerning the unmodelled dynamics.