  Electron tunneling through mesoscopic metallic grains can be treated
perturbatively only provided the tunnel junction conductances are sufficiently
small. If it is not the case, fluctuations of the grain charge become strong.
As a result (i) contributions of all -- including high energy -- charge states
become important and (ii) excited charge states become broadened and
essentially overlap. At the same time the grain charge remains discrete and the
system conductance $e$-periodically depends on the gate charge. We develop a
nonperturbative approach which accounts for all these features and calculate
the temperature dependent conductance of the system in the strong tunneling
regime at different values of the gate charge.
