A nasal cannula for supplying a respiratory gas to a patient, the nasal cannula comprising: a pair of supply lines which each expands in size, adjacent one end thereof, so as to form a head and the head contains a discharge opening therein for discharging a respiratory gas, and the opposite end of each of the pair of supply lines being connectable to a respiratory gas source; wherein each head is sized to be snugly received and retained within one of the nasal cavities of the patient; the pair of supply lines, adjacent the heads, being connected to one another by a central bridge member; each head being substantially cylindrical and having at least one elongate trough in an exterior surface thereof, the or each trough extends parallel to, but spaced from, a longitudinal axis of the end of the supply line; each elongate trough, once inserted into the respective nasal cavity of a patient, forming a leakage passage, between a portion of inwardly facing nasal cavity skin of a patient and a portion of an exterior surface of the head, to facilitate exhausting of any excess respiratory gas supplied to the patient through the leakage passage; and also facilitate inhalation of any room air required in excess of the respiratory gas to be supplied to the patient: wherein each head has a maximum width dimension of between about 0.88 cm (0.345 of an inch) and about 1.8 cm (0.70 of an inch) and a length of between about 0.76 cm (0.30 of an inch) and about 1.5 cm (0.60 of an inch); and each of the elongate troughs is formed by a pair of adjacent planar side surfaces which diverge away from a common elongate valley toward a pair of spaced apart but adjacent elongate ridges having maximum outside diameters coequal with the maximum outside diameter of each head to partially define one of the plurality of leakage passages in an exterior surface of the head. a pair of supply lines which each expands in size, adjacent one end thereof, so as to form a head and the head contains a discharge opening therein for discharging a respiratory gas, and the opposite end of each of the pair of supply lines being connectable to a respiratory gas source; wherein each head is sized to be snugly received and retained within one of the nasal cavities of the patient; the pair of supply lines, adjacent the heads, being connected to one another by a central bridge member; each head being substantially cylindrical and having at least one elongate trough in an exterior surface thereof, the or each trough extends parallel to, but spaced from, a longitudinal axis of the end of the supply line; each elongate trough, once inserted into the respective nasal cavity of a patient, forming a leakage passage, between a portion of inwardly facing nasal cavity skin of a patient and a portion of an exterior surface of the head, to facilitate exhausting of any excess respiratory gas supplied to the patient through the leakage passage; and also facilitate inhalation of any room air required in excess of the respiratory gas to be supplied to the patient: wherein each head has a maximum width dimension of between about 0.88 cm (0.345 of an inch) and about 1.8 cm (0.70 of an inch) and a length of between about 0.76 cm (0.30 of an inch) and about 1.5 cm (0.60 of an inch); and each of the elongate troughs is formed by a pair of adjacent planar side surfaces which diverge away from a common elongate valley toward a pair of spaced apart but adjacent elongate ridges having maximum outside diameters coequal with the maximum outside diameter of each head to partially define one of the plurality of leakage passages in an exterior surface of the head. wherein each head has a maximum width dimension of between about 0.88 cm (0.345 of an inch) and about 1.8 cm (0.70 of an inch) and a length of between about 0.76 cm (0.30 of an inch) and about 1.5 cm (0.60 of an inch); and each of the elongate troughs is formed by a pair of adjacent planar side surfaces which diverge away from a common elongate valley toward a pair of spaced apart but adjacent elongate ridges having maximum outside diameters coequal with the maximum outside diameter of each head to partially define one of the plurality of leakage passages in an exterior surface of the head.