Socioeconomic status is well known to be associated with inverse gradients in a wide range of health outcomes. Very little is known about the precise shape of these relationships and how they evolve through the life-course, although recent work has suggested steep non-linearities for mortality in samples of the entire population that include the very poor. We investigate the shape of gradients, against baseline family income, in gender-specific prevalence rates for seven self-reported health outcomes commonly used on surveys, in a cohort of 1190 men and 1302 women representative of Alameda County, California, aged 40-59 in 1965. Over 29 years of follow-up, four different prevalence-income gradients among surviving subjects are examined as this cohort has aged, in 1965, 1974, 1983 and 1994. Virtually all the gradients are inverse, although there is no simple pattern of shape, or evolution of shape over time, across health outcomes. However, there is a consistent trend for male gradients to be distinctly more non-linear than female gradients, such that the poorest men show disproportionately higher rates of ill health, based on generalized linear piecewise regression models, comparing the low versus high-income slopes of the gradients. However, sub-analyses of only those long-lived cohort members, who survived through all follow-ups, largely abolished the non-linearities in the male prevalence curves (except for "self-assessed health status" and "depression"), making them much more like female curves. This suggests that for all of these common forms of morbidity, the excess prevalence among very low income males was associated with elevated mortality. Confirmation of this observation must await richer data on other aspects of socioeconomic status in comparable cohorts, analyzed with similar methods.