  We provide analytical results for the perturbative correction to the
current-voltage relation through a vibrating molecule for weak electron-phonon
coupling. The nonlinear conductance exhibits a step-like feature at $eV=\hbar
\omega_0$, where $\omega_0$ is the vibration frequency. We establish criteria
for the sign change of the step in the conductance (up or down). This
transition turns out to be nonuniversal and is governed by essentially all
system parameters.
