Evidence that inflammatory mechanisms contribute to neuronal injury in Alzheimer's disease along with a number of epidemiological studies suggests that non-steroidal anti-inflammatory drugs (NSAIDs) may slow the rate of cognitive deterioration. We have selected two such drugs for a therapeutic trial: rofecoxib and naproxen. The trial employs a double-blind parallel design with three primary treatment groups: rofecoxib, naproxen and placebo. A total of 320 patients will be enrolled in the trial and randomized to the three groups. Stable use of cholinesterase inhibitors, estrogen, low dose aspirin, and vitamin E will be allowed. Patients with inflammatory diseases that might respond to the study medications will be excluded.