This paper proposes a strategy referred to as stability overlay (SO) for linear and nonlinear time-varying plants, that provides input/output stability guarantees for a wide set of adaptive control schemes. We use this methodology to endow multiple-model adaptive control (MMAC) architectures with robust stability properties when the plant to be controlled is uncertain and time-varying. We emphasize that adaptive control strategies should be able to handle time-varying plants, since these methodologies are usually applied to plants with drifting parameters. The results presented herein clearly indicate that multiple-model strategies augmented with the SO for time-varying plants ensure stability of the closed-loop for a wide class of disturbances and model uncertainty, while providing high performance capabilities whenever the stabilizing controllers have been designed for performance-robustness.