Using nonequilibrium perturbation theory, we investigate the nonlinear transport through a quantum dot in the Kondo regime in the presence of a magnetic field. We calculate the leading logarithmic corrections to the local magnetization and the differential conductance, which are characteristic of the Kondo effect out of equilibrium. By solving a quantum Boltzmann equation, we determine the nonequilibrium magnetization on the dot and show that the application of both a finite bias voltage and a

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... agnetic field induces a novel structure of logarithmic corrections not present in equilibrium. These corrections lead to more pronounced features in the conductance, and their form calls for a modification of the perturbative renormalization group.