Effects of the charging and single-electron tunneling in a cluster structure are investigated theoretically. In the framework of the particle-in-a-box model for the spherical and disk-shaped gold clusters, the electron spectrum and the temperature dependence of the electron chemical potential are calculated. Difference between the chemical potentials of massive electrodes and island's one leads to its charging. We show that the effective residual charge is equal to the non-integer value of elementary ch arge e and depends on the cluster's shape. The equations for the analysis of the current-voltage characteristic are used under restrictions associated with the Coulomb instability of a cluster. For single-electron molecular transistors the nonmonotonic size dependences of current gap and its voltageasymmetry are computed. We suggest that an overheating of electron subsystem leads to the disappearance of a current gap and gradual smoothing of current-voltage curves that is observed experimentally.