The conductance of two conducting dots coupled by very small capacitances is calculated. It shows remarkable structure as a function of a gate-induced potential Vg. At temperatures just below the Coulomb blockade energy, the conductance is found to oscillate periodically with Vg. As the temperature is reduced, however, the periodic oscillations give way to quasi-random conductance peaks. This behavior is a result of the incommensurate energy scales required to add charges to the two dots. © 1992 IOP Publishing Ltd.