They are called the bronchiThe smallest [air] tubes in the lungs are the broncioles they terminate the larger bronchi.Inside your lungs the two bronchi tubes divide into small bronchial tubes. The bronchial tubes then divide into bronchioles, which are even smaller air passages. Tiny air sacs, called alveoli, are on the ends of the bronchioles.The small tubes located within the lungs are known as the bronchial tubes. The bronchial tubes function is to purify the air that is going into the lungs, when the bronchial tubes become inflamed and swell, Asthma attacks can occur.