A new design approach is proposed for multivariable model reference adaptive systems, making use of linear feedback on the error signal, with augmentation of the linear compensator by nonlinear adaptation laws only if the linear compensation is inadequate for the task at hand. The determination of the required linear compensation is considered, and a multivariable frequency-domain performance criterion is developed. This performance criterion is then related to other scalar frequency-domain performance criteria. A new design method is outlined using the direct Nyquist array, and is then illustrated by application to a 2-input/2-output multivariable system with parameter uncertainty.