This paper looks in detail at Erasistratus of Ceos' theory of the triplokia, or 'triple web', of arteries, veins and nerves. It seeks to identify and remove some uncertainties about the nature of this theory and the problems it was intended to resolve, and to locate it more firmly within the context of his groundbreaking physiology. I argue that it was not a kind of elemental theory intended to describe what the body is ultimately composed of, but principally an account of how the arterial, venous and nervous systems interact with each other and the body's organs at a subsensible level.