Will life expectancy in the United States and other developed countries level off at about 85 years or continue to increase to a century or more? This research project is designed to address this controversy through theory-based model building and statistical analysis of two data sets -- from the U.S. and Sweden - - that will be rigorously checked for reliability an published in full to aid future researchers. Specifically, the proposed research will: (1) specify mathematical models that are consistent with the underlying concepts of the alternative "limited-lifespan" and "mortality-reduction" paradigms: (2) contrast the implications of the models about (a) the shape of the age-trajectory of the force of mortality at advanced ages, and (3) compile, critically examine, and publish in full two data sets on age-specific mortality at older ages, pertaining to Sweden and to U.S. medicare enrollees: and (4) using maximum likelihood estimation, determine how well the alternative models fit the date.