  In this paper we give a smooth linearization theorem for nonautonomous
differential equations with a nonuniform strong exponential dichotomy. In terms
of discretized evolution operator with hyperbolic fixed point 0, we formulate
its spectrum and then give a spectral bound condition for the linearization of
such equations to be simultaneously differentiable at 0 and H\"older continuous
near 0. Restricted in the autonomous case, our result is the first one that
gives a rigorous proof for simultaneously differentiable and H\"older
linearization of hyperbolic systems without any non-resonant conditions.
