An adjustable headgear for use with reusable or disposable nasal and/or oral gas delivery masks. The headgear includes a cap-like headpiece adapted to fit the crown and back of a patient's head. Lower strap means provide a two-point connection with the gas delivery mask to achieve a comfortable fit and an effective seal. Depending strap means depending from the head piece are connected to and moveable relative to the lower strap means. The depending strap means offer a stabilizing connection between the head piece and the lower strap means. Upper strap means can be used in the event an effective seal cannot be achieved using only the lower strap means. The upper and lower strap means provide a four-point connection with the gas delivery mask.