  In a quantum Hall interferometer, the dependence of the signal on
source-drain voltage is controlled by details of the edge physics, such as the
velocities of edge modes and the interaction between them and with screening
layers. Such dependence of the signal has been seen in recent experiments at
various integer and fractional filling factors, including $\nu=2$ and $\nu=2/5$
where two edge modes are present. Here we study theoretically the
current-voltage curves for various values of the relative edge velocities,
interaction strength and the temperature, in a model containing two edge modes.
We consider separate cases where the inner mode or the outer mode is weakly
backscattered at the tunneling contacts. When the inner mode is completely
reflected and the outer mode is partially transmitted, we find striking
features at very low temperatures related to resonance of excitations of the
closed inner channel. Fluctuations in the charge of the closed inner mode,
caused by sparse tunneling events, lead to an exponential suppression of the
interference visibility at high voltages, in agreement with experiments.
