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The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ℒp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform (μ,ν) contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform (μ,ν) contraction and dichotomy is provided.