<p>Takens theorem for a partially hyperbolic dynamical system provides a normal linearization along the center manifold. In this paper, we give the nonautonomous version of Takens theorem under non-resonance conditions formulated in terms of the dichotomy spectrum. In our proof, one difficulty is solving homological equations for the normal form theory which involve a center variable, while another difficulty is finding the dichotomy spectrum of a certain matrix cocycle that is block lower triangular. In order to overcome those difficulties, in comparison with the autonomous case, we need an additional term in the (nonautonomous) non-resonance conditions to guarantee certain spectral gap conditions. This additional term disappears naturally in the autonomous case.</p>