This is designed as a pilot (preliminary) study to evaluate the differences in effects on attention, sleep problems and gastrointestinal tolerance associated with Alzheimer's Disease with two different drugs at two different doses. Patients must have mild to moderate Alzheimer's Disease based on the National Institute of Neurological and Communicative Disorders and Stroke-Alzheimer's Disease and Related Disorders Association (NINCDS-ADRDA) criteria and a Mini-Mental State Examination (MMSE) score of 10 to 24. The trial will consist of a 2-week run-in phase, an 8-week assessment phase, and an extension phase of variable length (6 weeks to 54 weeks). During the study, patients will be randomized (assigned by chance) to receive either galantamine or donepezil. Galantamine will be given by mouth 4mg twice daily for Weeks 1-4 and then 8mg twice daily for Weeks 5-8 and beyond (for participants in the extension). The patients on donezepil will receive 5mg by mouth at bedtime for Weeks 1-4 and then 10mg at bedtime for Weeks 5-8 and beyond. Placebo tablets will be given so that each patient takes two capsules per dose in order to conceal the identity of the drugs. Neither the patient nor the physician will know which drug the patient is receiving. Drug effectiveness will be measured by change in overall functioning of the patient shown by the Clinician's Interview-Based Impression of Change Plus Family Input (CIBIC-Plus). Other tests to evaluate whether the drug is effective will include the change in results of attention tests (Simple Reaction Time [SRT], Choice Reaction Time [CRT], Verbal Series Attention Test [VSAT], and Stroop Test), and in sleep pattern tests (tests that measure movements during sleep [Actiwatch] and patterns of sleep such as the caregiver-completed Pittsburgh Sleep Quality Index [PSQI] and the Circadian Sleep Inventory for Normal and Pathological States [CSINAPS]). Measures of quality of life will include the Alzheimer's Disease Related Quality of Life Scale (ADRQL) and the caregiver-completed Allocation of Caregiver Time Survey (ACTS) and SF-12 Quality of Life Survey. Safety assessment and gastrointestinal tolerability will be based on recording the number and severity of unexpected and undesirable events as well as physical examination and vital signs. The exploratory study hypotheses are that galantamine will be superior to donezepil in improving attention, sleep patterns, and quality of life in patients with mild-to-moderate Alzheimer's disease and that it will be well tolerated by patients.