Previous studies have established that testosterone replacement in older men with low testosterone levels increases muscle mass and strength. However, lack of information in two areas has prevented formulation of general recommendations about wider use of testosterone replacement in older men. First, the effectiveness of testosterone in improving physical function, quality of life, and other health-related outcomes has not been demonstrated. Second, while there is agreement that short-term administration of testosterone in replacement doses is safe, the long-term risks of testosterone supplementation in older men remain unknown. The areas of major concern are the risks of prostate cancer and heart disease. Because of the high prevalence, even small increases in the incidence rates of atherosclerotic heart disease associated with testosterone supplementation will have significant impact on overall morbidity and mortality, and health care costs. The study will evaluate one important aspect of the long-term safety of testosterone administration by directly examining its effects on the rate of progression of atherosclerosis. If the study demonstrates that testosterone retards atherosclerosis progression, then that would provide one additional reason for testosterone supplementation of older men with low testosterone levels. If the study demonstrates a neutral effect of testosterone on atherosclerosis progression, that information would also be reassuring and useful to regulatory agencies. This study will establish the efficacy of testosterone replacement in improving physical, sexual and cognitive functions that are major determinants of health-related quality of life in older men.