Electron tunneling through mesoscopic metallic grains can be treated p
erturbatively only provided the tunnel junction conductances are suffi
ciently 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 depe
nds on the gate charge. We develop a nonperturbative approach which ac
counts 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.