For most of the 20th century the sex gap in life expectancy in the industrialized countries has widened in favor of women. By the early 1980s a reversal in the long-term pattern of this differential had occurred in some countries, where it reached a maximum and thereafter followed a declining trend. Of particular interest to the present investigation is the anomalous experience of Japan, where unlike other high-income countries the female advantage in life expectancy has been expanding. We contrast the case of Japan with that of Sweden, where, like many other high-income nations, the sex differential in longevity has been narrowing in recent years. We observe that in Sweden, until the early 1980s, the sex gap in life expectancy (female-male) exceeded that of Japan; but this situation reversed in subsequent periods, when the Swedish differential narrowed and that of Japan widened. A decomposition analysis indicates that these divergent patterns since 1980 have resulted mainly from larger than expected reductions in male mortality in Sweden due to heart disease and from accidents and violence, lung cancer and "other" cancers. In Japan, death rates for men and women from heart disease--which is a leading cause of death--have tended to decline more or less at the same pace since the early 1980s; and with regard to lung cancer, and "other" neoplasms, male death rates in Japan have been rising while those of women have either declined or risen more slowly. Moreover, during the 1990s, male and female suicide rates rose in Japan, but the rates for men went up faster. Altogether, the net effect of these divergent mortality trends for men and women in Japan underlie much of the observed widening of its sex differential in longevity in recent years.