We study long-term trends in regional car travel demand within and across socio-demographic groups in Sweden, using cross-sectional data from National Travel Surveys, spanning the period from 1978 to 2011. We find that the reduction in per-adult driving in Sweden mainly occurs among urban men. Urban men of all income groups reduced their driving for both commuting and non-commuting trips in conjunction with rising gasoline prices, which may have contributed to this development. We find that driving among those socio-demographic groups, who have better opportunities to reduce their driving, and driving for discretionary rather than commute purposes is being reduced over time. Sweden is ranked among the most gender-equal countries in the world; yet we find a substantial remaining gender gap in the share of adults driving a car on an average day, even when controlling for other socio-economic differences.