  We calculate the 2-loop partition function of QCD on the lattice, using the
Wilson formulation for gluons and the overlap-Dirac operator for fermions.
Direct by-products of our result are the 2-loop free energy and average
plaquette. Our calculation serves also as a prototype for further higher loop
calculations in the overlap formalism. We present our results as a function of
a free parameter $M_0$ entering the overlap action; the dependence on the
number of colors $N$ and fermionic flavors $N_f$ is shown explicitly.
