The delivery system has a control body in the form of a pendant to which oxygen is delivered and from which the oxygen is delivered to the patient. The body includes a reservoir which has a constant oxygen supply orifice. During rest conditions, the patient breathes only a portion of the reservoir contents. During physical activity, the patient breathes more deeply and inhales more oxygen from the reservoir. The reservoir has a flexible diaphragm and when breathing more deeply, the diaphragm moves to open a bolus oxygen supply valve to introduce a bolus of additional oxygen to the reservoir and thus to the patient.