This project is designed to study whether anti-inflammatory drugs, such as celecoxib, may delay age-related mental decline. We are also looking at genetic risk and brain structure as potential predictors of mental decline. We believe people with age-associated memory impairment who take celecoxib will show less evidence of mental decline than those receiving placebo (an inactive pill) after 18 months. We expect that brain structure at the start of the study, memory performance as indicated by tests, and age will be additional predictors of mental decline. We also predict that cognitive decline (i.e., decline in thinking and memory) and treatment response will vary according to genetic factors that may correlate with the age at which dementia begins. We believe other variables such as prior educational achievement, memory capability at the outset of the study, and gender may influence mental decline and treatment response. We will study people with age-associated memory impairment (mild memory complaints, decreased performance in selected memory tests), between 40 and 90 years of age. The subjects will be randomly (i.e., by a process similar to flipping a coin) assigned to treatment groups. The subjects will receive either an inactive substance (placebo) or celecoxib (400 mg/day). The subjects will receive a magnetic resonance imaging (MRI) scan, FDG PET scan, routine laboratory blood tests, electrocardiogram and cognitive tests. They will be followed for approximately 18 months and asked to return at specific intervals for follow-up testing. Measures of brain structure will be derived from baseline MRI scans and metabolic activity from PET scans, and blood will be drawn and tested to determine which forms (genotypes) of certain genetically determined cellular components the patient has.