Primary Objectives To determine, in a population of 5-9 year old children with asthma, if regular use of either of two classes of anti-inflammatory medications (inhaled corticosteroids or cromolyn sodium), compared to regular bronchodilator medication and to each other, results in greater lung function and less bronchial hyperresponsiveness over a five year period. Secondary Objectives To determine if either of the anti-inflammatory medications, compared to bronchodilator medication and to each other, results in less patient morbidity, measured by frequency of asthma symptoms, days of limited activity, and days lost from school. To determine if either of the anti-inflammatory medications compared to regular bronchodilator medication and to each other results in less use of health care resources such as emergency room visits or hospitalizations. To compare the long term safety and side effects of the two classes of anti-inflammatory medications, compared to bronchodilator medication and to each other. To compare the effects of the two classes of anti-inflammatory medications, compared to bronchodilator medication and to each other, on physical and psychosocial development, and on quality of life.