The design and complete stability analysis for the model reference adaptive control (MRAC) of multivariable plants with input and/or output delays are presented in this paper. A modified estimation error, which enables us to solve the non-commutativity problem and the stability issue in the multivariable case, is introduced in the adaptive law for updating the controller parameters. A generalized controller structure, which achieves stable model-plant transfer matrix matching in the presence of delays, is developed for the multivariable MRAC scheme. Based on a unified framework it is shown that the proposed adaptive control scheme guarantees the global stability and asymptotic zero tracking error for the closed-loop system.