This study will include the patients who are Japanese children with bronchial asthma aged 5 years to 15 years old and have completed the Phase III study (Study code: D5254C00769) at about 29 centres. To investigate the safety of budesonide Turbuhaler® with a daily dose of 100 µg to 800 µg for 54 weeks treatment including the prior 6 weeks Phase III study (Study D5254C00769, NCT00504062) as compared with conventional therapy in Japanese children with bronchial asthma in need of inhaled glucocorticosteroid treatment.