  We study the stability of the normal state in a mesoscopic NSN junction
biased by a constant voltage V with respect to the formation of the
superconducting order. Using the linearized time-dependent Ginzburg-Landau
equation, we obtain the temperature dependence of the instability line,
V_{inst}(T), where nucleation of superconductivity takes place. For
sufficiently low biases, a stationary symmetric superconducting state emerges
below the instability line. For higher biases, the normal phase is destroyed by
the formation of a non-stationary bimodal state with two superconducting nuclei
localized near the opposite terminals. The low-temperature and large-voltage
behavior of the instability line is highly sensitive to the details of the
inelastic relaxation mechanism in the wire. Therefore, experimental studies of
V_{inst}(T) in NSN junctions may be used as an effective tool to access
parameters of the inelastic relaxation in the normal state.
