  Measurements of elastic and inelastic cotunneling currents are presented on a
two-terminal Aharonov--Bohm interferometer with a Coulomb blockaded quantum dot
embedded in each arm. Coherent current contributions, even in magnetic field,
are found in the nonlinear regime of inelastic cotunneling at finite bias
voltage. The phase of the Aharonov--Bohm oscillations in the current exhibits
phase jumps of $\pi$ at the onsets of inelastic processes. We suggest that
additional coherent elastic processes occur via the excited state. Our
measurement technique allows the detection of such processes on a background of
other inelastic current contributions and contains information about the
excited state occupation probability and the inelastic relaxation rates.
