This analysis aims to get a step further in the understanding of the determining factors of social health inequalities, and to explore particularly the role played by parents' social status and their vital status or age at death on the social health inequalities in adulthood among European older adults. The wealth-related health inequalities are measured using the popular concentration index. We then implement the decomposition method of the indices and evaluate the contribution of the various determinants of health introduced in interval regression models. Health is measured using self-assessed health and country-specific cut-points that correct observed differences in self-report due to cross-cultural differences in reporting styles. This paper uses data for ten European countries from the first wave of the 2004 SHARE. The study highlights significantly higher wealth-related health inequalities in the Netherlands, Denmark and Germany. These social inequalities of health in Europe are explained largely by individuals' current social conditions, particularly wealth. Nevertheless, our analysis attests the existence of a long-term influence of initial conditions in childhood on health in middle-aged and beyond, independently of current social characteristics, which contribute to differences in health status across social groups. This article contributes to the identification of social determinants, which are important determinants of health and follows recommendations suggested to help 'close the gap' in various health inequities.