The I-V characteristics of two serially coupled small tunnel junctions (about ${10}^{\mathrm{\ensuremath{-}}18}$--${10}^{\mathrm{\ensuremath{-}}19}$ F capacitances) are measured at 4 K. The junctions are formed using a scanning-tunneling microscope to probe a metal droplet deposited on an oxidized metal substrate. Sharply defined Coulumb steps due to single-electron dynamics, oxide polarization, and nonlinear (voltage dependent) tunneling rates are observed. The results show very good quantitative agreement with theoretical calculations based on the semiclassical picture.