This study examines whether the racial disparity in functional health grows unabated over the adult life course--the cumulative disadvantage hypothesis--or shrinks among the oldest old---the age-as-leveler hypothesis. Special emphasis is placed on the role of socioeconomic status (SES), which is highly associated with race. The analysis uses latent growth-curve modeling to examine differences in age trajectories of functional health between Black and White Americans and is based on nationally representative panel data of 3497 adults. Results cautiously support the age-as-leveler hypothesis. Net of functional health at baseline, Black adults experience a growing disadvantage in functional health over time until the oldest ages, when the gap in functional health begins to shrink. Results indicate that the potential leveling mechanisms of age may be specific to women. SES including financial assets explains the divergence in functional health across young and middle-aged Black and White adults, but not the later-life convergence. This study reveals the life-course pattern of racial disparity in functional health and suggests that more theoretical development is needed in this field to explain why the age-as-leveler and cumulative disadvantage processes are different for functional health than for other outcomes.