  We describe single electron tunneling through molecular structures under the
influence of nano-mechanical excitations. We develop a full quantum mechanical
model, which includes charging effects and dissipation, and apply it to the
vibrating C$_{60}$ single electron transistor experiment by Park {\em et al.}
{[Nature {\bf 407}, 57 (2000)].} We find good agreement and argue vibrations to
be essential to molecular electronic systems. We propose a mechanism to realize
negative differential conductance using local bosonic excitations.
