Nonlinear singularly perturbed diff. erential equations with two natural time scales are under consideration. It is shown that the exponential stability of both the boundary layer systems and the reduced system imply the exponential stability of the fully coupled system for small perturbation parameters. The asymptotic behavior of gain and decay rates is investigated. Moreover, it turns out that the achieved exponential stability is robust with respect to multivalued regular perturbations and small delays. The method of proof does not rely on (converse) Lyapunov theorems but on an appropriate version of Tychonov's theorem and manages without the smoothness of the vector fields involved.