This paper demonstrates that, over the period 1948-2003, sex differentials in mortality in the age range 50-54 to 85+ widened and then narrowed on a cohort rather than on a period basis. The cohort with the maximum excess of male mortality was born shortly after the turn of the century. Three independent sources suggest that the turnaround in sex mortality differentials is consistent with sex differences in cigarette smoking by cohort. An age/period/cohort model reveals a highly significant effect of smoking histories on men’s and women’s mortality. This model suggests that improvements in mortality at older ages are likely to accelerate in the future.