The invention concerns a gaseous medicine comprising a mixture of nitrogen monoxide (NO) and nitrogen (N2) for use by inhalation for the treatment of hypoxemic respiratory failure linked to pulmonary vasoconstriction in humans, said gaseous mixture containing between 1200 and 4500 ppm by volume (ppmv) of nitrogen monoxide (NO) and said hypoxemic respiratory failure being chosen from acute respiratory distress syndrome (ARDS) or persistent pulmonary hypertension of the newborn infant (PPHN).