The maximum daily dosage of Aleve varies according to the treated affliction and is usually a maximum of 1,500 milligrams for limited periods of time. Initial doses vary between 500 and 1,000 milligrams per day. Aleve is a nonsteroidal anti-inflammatory drug, or NSAID, whose main ingredient is naproxen, states Drugs.com.
Patients should check with their doctors before taking Aleve if they smoke or they have a history of heart problems, stomach disorders, kidney or liver disease, asthma, nasal polyps or blood clotting disorders, states Drugs.com. Side effects of Aleve may include chest pain, difficult breathing, weakness, abnormal stools, nausea, bruising, fever, headaches or severe skin reactions.