A novel biphasic pharmaceutial or nutraceutical composition delivers both an immediate and a sustained dose of a pharmaceutical or nutraceutical agent in the same unit dose. An oral unit dose of melatonin includes melatonin in a sustained-release matrix contained in a solid phase, such as a tablet of capsule, and also includes melatonin in a film dispersed on the surface of the solid phase. Approximately 80 to 90 weight percent of the total amount of melatonin of each unit is contained in the sustained-release matrix and the remainder in the film. The novel composition permits a mammal, including a human being, to both rapidly fall asleep and remain asleep for a desired period of time by releasing an immediate-release dose and a sustained-release dose of melatonin.