The variable structure model-reference adaptive control (VS-MRAC) redesign and stability analysis, presented earlier for the case of plants with relative degree n* less than or equal to 2, is generalized to the case of arbitrary n* greater than or equal to 1. This paper presents a complete stability analysis in the general case. The redesign is based on the explicit consideration of input disturbances which may include the disturbance originated by the uncertainty of the plant high-frequency gain. This leads to a considerably simpler and less restrictive stability analysis as well as to a systematic controller design for external disturbance rejection. The overall error system is globally exponentially stable with respect to a small residual set, Robustness to unmodeled dynamics is also discussed.