We examine how intergenerational income mobility responds to structural changes in a simple theoretical model of intergenerational transmission, deviating from the existing literature by explicitly analyzing the transition path between steady states. We find that mobility depends not only on current but also on past transmission mechanisms, such that changing policies, institutions or economic conditions may generate long-lasting trends. Variation in mobility levels across countries may thus be partly explained by differences in former institutions; current mobility trends may be caused by institutional changes in the past. We further find that transitions between steady states tend to be non-monotonic. Changes in the relative returns to different skills or a shift towards a less plutocratic and more meritocratic economy raise mobility initially, but also generate a negative trend over subsequent generations. Times of change thus tend to be times of high mobility, and declining mobility today may not reflect a recent deterioration of equality of opportunity but rather major improvements made in the past.