  We analysed the electron-hole or, in another words, branch imbalance (BI) and
the related electric potential $V_{imb}$ which may arise in a mesoscopic
superconductor/normal metal (S/N) structure under non-equilibrium conditions in
the presence of a supercurrent. Non-equilibrium conditions can be created in
different ways: a) a quasiparticle current flowing between the N reservoirs; b)
a temperature gradient between the N reservoirs and no quasiparticle current.
It is shown that the voltage $V_{imb}$ oscillates with the phase difference
$\phi$. In a cross-geometry structure the voltage $V_{imb}$ arises in the
vertical branch and affects the conditions for a transition into the
$\pi$-state.
