A respiratory triple swivel manifold is provided which has a base port, which is coupled to a central body. The central body has two laterally-positioned arms, and each arm has a lateral port. Each base port and each lateral port has an inner sleeve which is movable relative to its port. The manifold also has a proximal port coupled to the central body, which may or may not have a rotatable inner sleeve. At least one of the arms and its respective lateral port is positioned at an angle in a range of greater than 90 degrees but less than 180 degrees relative to the central body. Desirably, the base port, the central body and its arms and their respective ports form a Y-shape. The proximal port may intersect the Y-shaped manifold. The base port includes a ramp to direct an object moved through one port into a passageway of the manifold and through the base port to an endotracheal tube without folding, twisting or bunching of any portion of the object within the manifold.