An apparatus for delivering continuous positive airway pressure to a patient (e.g., an infant) includes a cradle assembly for firmly and adjustably supporting the head of a patient to whom continuous positive airway pressure is to be delivered, a support frame assembly mounted on the cradle assembly for adjustably supporting a disposable airway set, and a disposable airway set which receives fresh air and delivers it, under pressure, to a patient. The cradle assembly includes a head-supporting cradle which may be moved to any one of a number of angular positions. A pair of adjustable head-restraining plates are mounted in the cradle for firmly supporting heads of different sizes. The support frame assembly which receives and holds the disposable airway set is mounted on one end of the head-supporting cradle and can be adjusted relative to the cradle for accurate positioning of a nasal cannula at the delivery end of the disposable airway set. The support frame assembly includes a swingable support arm which receives and retains the disposable airway set. The swingable support arm may be swung to a position wherein the disposable airway set retained therein may be swung out of the vicinity of the patient's head to facilitate insertion and removal of the patient's head and treating of the patient. The disposable airway set includes a pop-off valve assembly for limiting the maximum amount of pressure of the air delivered to the patient and a pressure control valve for controlling the pressure of the air delivered to the patient. The disposable airway set is comprised of two airway arms which are connected to one another by a connector member which establishes fluid communication between the two arms. One end of one of the airway arms of the disposable airway set receives fresh air from an air supply, and the other end of the first arm has a re-breather bag connected thereto for "bagging" the patient. One end of the second airway arm is provided with a nasal cannula for attachement to the patient, and the other end of the second arm is provided with the pressure control valve. The disposable airway set is adapted to be used for one patient only, and discarded after use.