  We study quasi-one dimensional wires of two-band superconductors driven by an
electrical current. We find that the onset of dissipation can occur with the
nucleation of time-connected phase slips (t-PS). The topological structure of
the t-PS consists of two phase slips (one in each order parameter) separated in
time and connected via an interband vortex string along the time direction.
This shows as a two-peak structure in voltage vs. time. We discuss the
conditions for observing t-PS, depending on the interband coupling strength and
the relaxation time scales for each order parameter.
