This paper presents the first national-level econometric estimates of the residential energy demand system for Australia. We estimate an Almost Ideal (AI) demand system for electricity, gas, and other miscellaneous fuels (mainly oil and wood) using quarterly data for both the country as a whole and for a panel of the five most populous States. The national data set covers the period from 1969 Q3 to 1998 Q2, while the state level data is only available from 1984 Q3 onwards. According to the national-level data, the pairs of electricity and miscellaneous fuels and gas and miscellaneous fuels are significant substitutes, whereas electricity and gas - the two main fuels - may be complements. The panel model, in contrast, finds significant substitution possibilities between gas and miscellaneous fuels only. The cross-price elasticities between electricity and gas are positive but not significant. The gas own-price elasticity is zero in the national model and unit elastic in the panel model. A national model estimated over the same shorter time period still shows complementarity between electricity and natural gas but most results are insignificant. Both large time-series and cross-sectional dimensions are valuable in estimating elasticities. Compared to North American estimates, our results show greater own price and income elasticities for natural gas and the miscellaneous category. They also show more substitutability between natural gas and the miscellaneous category.