  Effects of a coupling between the mechanical vibrations of a quantum dot
placed between the two leads of a single electron transistor and coherent
tunneling of electrons through a single level in the dot has been studied. We
have found that for bias voltages exceeding a certain critical value a
dynamical instability occurs and mechanical vibrations of the dot develop into
a stable limit cycle. The current-voltage characteristics for such a transistor
were calculated and they seem to be in a reasonably good agreement with recent
experimental results for the single $C_{60}$-molecule transistor by Park et
al.(Nature {\bf 407,} (2000) 57).
