OUTLINE: Patients receive doxorubicin hydrochloride IV, bleomycin sulfate IV, vinblastine IV, and dacarbazine IV (ABVD) on days 1 and 15. Treatment repeats every 28 days for 3 courses. On day 15 of the third course of chemotherapy, patients undergo a CT scan of the neck, thorax, abdomen and pelvis. Patients with nonresponsive disease or progressive disease are removed from the study. Patients who achieve response undergo fludeoxyglucose F 18 positron emission tomography (FDG-PET). Patients with a positive FDG-PET scan receive an additional course of ABVD and undergo involved field radiotherapy. Patients with a negative FDG-PET scan are randomized to 1 of 2 treatment arms.