Let (X^e)_t be the result of perturbations of a dynamical system

(semiflow, stochastic process) X_t. The parameter e<<1 characterizes the size of perturbations in an appropriate metric; (X^e)_t converges to X_t s e->0. Long time behavior of (X^e)_t is of interest in many problems. But there are two large parameters here t and 1/e. The limit depends on how the point (t,1/e) approach the infinity. Under natural assumptions, one can consider fast and slow component of the perturbed system. The slow component, in an appropriate time scale approaches a motion on the simplex of probability invariant measures of the non-perturbed system. The fast component can be characterized by a corresponding invariant measure. There are some general results of this type. But I will consider from this point of view various concrete perturbation theory problems like perturbations of finite Markov chains, of various dynamical systems, second order PDEs with a small parameter, homogenization, wave fronts in Reaction-Diffusion equations.