Abstract: A perturbation analysis is introduced to analyze the slow-drift of MRAC in the mean balancing position with normal zero mean noise and unmodeled dynamics. It is pointed out that the adaptive controller based on Lyapunov stability theory (or the hyperstability theory) completes the integration of the square term caused by the integration of the multiplication term, and the integration of the square term is exactly the source of the slow-drift and its instability. In the MRAC, it can be shown that the integrator and multiplication term must be canceled to obtain a favourable property.