In a previous 6-month study in patients with both vascular dementia and Alzheimer's dementia, galantamine demonstrated positive results on thinking, functioning, behavior, speech and overall well being of patients, and prevented the behavior symptoms of dementia from appearing. This combined study consists of two almost identical 26-week studies that examine the same criteria as the previous study, but in a larger patient population (dementia has been identified as having been caused by blood vessel disease without Alzheimer's disease). The study starts with a 4-week period in which current medications for dementia are withdrawn followed by a 26-week double-blind treatment period when patients will receive either placebo or galantamine 8 milligrams or 12 milligrams twice a day. Effectiveness will be measured by changes in scores on the Alzheimer's Disease Assessment Scale cognitive subscale, Alzheimer's Disease Cooperative Study Scale, the Clinician's Interview-Based Impression of Change Plus, and the neuropsychiatric inventory, as well as (in English-speaking countries only) a 10-minute interview of the patient (EXIT-25 scale). Safety will be evaluated throughout the study based on the incidence and severity of unexpected events, laboratory and physical tests, and vital signs. The hypothesis of the study is that galantamine will improve thinking, function, behavior, speech, and overall well being, better than placebo. A voluntary pharmacogenomic study will be incorporated into the study plan to evaluate whether specific genes are related to the dementia or drug response. 8 milligrams (mg) 2 times a day for 8 weeks, then increasing to12 mg, if tolerated. After 12 weeks dose can be reduced to 8 mg or matching placebo