A grandmother hypothesis may explain why humans evolved greater longevity while continuing to end female fertility at about the same age as do the other great apes. With that grandmother hypothesis in mind, we sought to compare age-specific mortality and fertility rates between humans and chimpanzees, our closest living relatives, and found two puzzles. First, we expected that lower adult mortality in humans would be associated with slower senescence, but the rate of chimpanzee demographic aging falls within the human range. Second, we expected declines in age-specific fertility to be similar in the two species but instead of falling in the thirties as it does in women, fertility remains high into the forties in some chimpanzee populations. We report these puzzles using data from nine human populations and both wild and captive chimpanzees, and suggest that systematic differences in the heterogeneity of surviving adults may explain them. Am. J. Hum. Biol., 2009. © 2009 Wiley-Liss, Inc.