The aim of this exploratory randomized, placebo controlled study is to evaluate the efficacy of Circadin® 2mg in patients with mild to moderate Alzheimer Disease (AD) treated with the acetylcholinesterase (AChE) inhibitor. The effects of add-on Circadin® 2mg vs. placebo on the decline in cognitive skills and global functioning, as well as on daytime somnolence and will be assessed.