By parameterising the Almost Ideal (AI) demand system as a vector error correction model (VECM), this paper estimates the structure of consumer energy demand in Australia. To this end, domestic per person expenditure on energy is divided into the expenditure on electricity, gas and a miscellaneous category, residual fuels. To close the system, non-energy household consumption expenditure is introduced, resulting in a four-equation share system, which is estimated using national-level quarterly data. The demand for electricity and gas is price and income inelastic whereas that of other fuels is highly price elastic. Significant substitution possibilities are found between electricity and other fuels and between gas and other fuels. However, electricity and gas – which, together, account for more than 90 per cent of household fuel expenditure – are estimated to be complementary fuels.