  We consider a tunnel junction formed between a fixed electrode and an
oscillating one. Accumulation of the charge on the junction capacitor induces a
force on the nano-mechanical oscillator. The junction is voltage biased and
connected in series with an impedance $Z(\omega)$. We discuss how the picture
of Coulomb blockade is modified by the presence of the oscillator. Quantum
fluctuations of the mechanical oscillator modify the $I$-$V$ characteristics
particularly in the strong Coulomb blockade limit. We show that the oscillator
can be taken into account by a simple modification of the effective impedance
of the circuit. We discuss in some details the case of a single inductance
$Z(\omega)=iL\omega$ and of a constant resistance $Z(\omega)=R$. With little
modifications the theory applies also to incoherent transport in Josephson
junctions in the tunneling limit.

Mesoscale and Nanoscale Physics