We have studied tunnelling between two quantum dots with a continuous densi
ty of states. The Coulomb blockade oscillations show a double peak structur
e when the transmission between the dots is below unity. This peak-splittin
g is described in terms of the electrostatic interaction between the two do
ts using a classical capacitance description. This model neglects charge fl
uctuations due to tunnel events between the dots. We compare the temperatur
e dependence of the split-peaks with a recent theory that does include char
ge fluctuations, (C) 1998 Academic Press.