It is shown how functional renormalization group methods in
imaginary time can be generalized to real times by formulating
them on a Keldysh contour. In addition we show how problems of
dissipative quantum mechanics can be treated where the local
degrees of freedom can not be integrated out (operator vertices).
To avoid singularities in the real-time flow and in order to
preserve causality we propose to use a cutoff-parameter in the
complex plane. The imaginary part of the cutoff corresponds to
the Matsubara frequencies of the Fermi functions and the real
part to the voltage. We apply the formalism to quantum transport
through interacting quantum wires with impurities (Luttinger
liquid) and to the nonequilibrium Kondo model. Within a general
microscopic theory we describe the cutoff of the RG flow by
voltage-induced energy broadening or relaxation/dephasing rates.
Furthermore we find that the voltage can influence the power law
exponents for the conductance through a quantum wire coupled to
reservoirs induced by nonequilibrium occupation probabilities.