We start from a general theory of intergenerational class mobility previously proposed as an alternative to the ‘liberal’ theory. In further evaluating these theories, we report empirical analyses of relations within the origins–education–destinations (OED) triangle, drawing on data for individuals born 1923–1977 in 17 European societies. In contrast with earlier research, we treat education in relative terms. We find that the tendency for fluidity to increase within class structures after World War II, rather than being the expression of a ‘worldwide secular trend’, was restricted to a distinctive historical period of rapid economic growth and class structural change. Furthermore, in accounting for this increasing fluidity, the role of education may easily be exaggerated. The weakening of the ‘direct’ OD association is of at least comparable importance to changes in the OE and ED associations. Consistently with the proposed theory, class structural change, insofar as it promotes greater upward mobility, would also appear to provide a favourable context for increasing fluidity. Where downward mobility increases, the growing motivation and the capacity of more advantaged parents to protect their children against déclassement constitutes a powerful source of resistance to change in endogenous mobility regimes.