  A systematic truncation of the many-body Hilbert space is implemented to
study how electrons in a quantum dot attached to conducting leads respond to
time-dependent biases. The method, which we call the dynamical 1/N approach, is
first tested in the most unfavorable case, the case of spinless fermions (N=1).
We recover the expected behavior, including transient ringing of the current in
response to an abrupt change of bias. We then apply the approach to the
physical case of spinning electrons, N=2, in the Kondo regime for the case of
infinite intradot Coulomb repulsion. In agreement with previous calculations
based on the non-crossing approximation (NCA), we find current oscillations
associated with transitions between Kondo resonances situated at the Fermi
levels of each lead. We show that this behavior persists for a more realistic
model of semiconducting quantum dots in which the Coulomb repulsion is finite.
