  We obtain a characterization of two classes of dynamics with nonuniformly
hyperbolic behavior in terms of an admissibility property. Namely, we consider
exponential dichotomies with respect to a sequence of norms and nonuniformly
hyperbolic sets. We note that the approach to establishing exponential bounds
along the stable and the unstable directions differs from the standard
technique of substituting test sequences. Moreover, we obtain the bounds in a
single step.
