OUTLINE: This is a randomized, multicenter study. Patients are stratified by center. Patients who are under age 40 and have lymphocyte-predominant or nodular sclerosing histology, an erythrocyte sedimentation rate less than 50, and fewer than 4 disease sites (supradiaphragmatic or pelvic node sites) are assigned to cohort 1 (good prognosis). All other patients are assigned to cohort 2 (poor prognosis). Cohort 1: Arm I: Patients with supradiaphragmatic disease undergo radiotherapy to the supradiaphragmatic lymph node areas (mantle region), spleen, and para-aortic lymph nodes 5 days a week for 4 weeks. Patients with pelvic disease undergo radiotherapy to an "inverted-Y" field (excluding the spleen) 5 days a week for 4 weeks. Arm II: Patients receive doxorubicin, bleomycin, vinblastine, and dacarbazine IV on days 1 and 15 (ABVD). Treatment continues every 4 weeks for a total of 2 courses in the absence of disease progression or unacceptable toxicity. Patients with complete remission (CR) after course 2 receive 2 additional courses past CR. Patients with partial remission (PR) after course 2 receive 4 additional courses past PR. Patients with unconfirmed/uncertain complete remission (CRu) receive 2-4 additional courses past CRu. Cohort 2: Arm III: Patients receive ABVD as in arm II, followed 4-6 weeks later by concurrent radiotherapy to the mantle region and upper abdomen to the level of L2 5 days a week for 4 weeks. Alternatively, radiotherapy may also be administered sequentially to the mantle region 5 days a week for 4 weeks and then to the upper abdomen to the level of L2 5 days a week for 4 weeks. Arm IV: Patients receive ABVD only as in arm II. Patients with disease progression after treatment in arms II or IV are considered for radiotherapy. Quality of life is assessed on day 1 of each course of chemotherapy (arms II-IV) and on day 28 of the last course of chemotherapy (arms II and IV); on the first and final days of radiotherapy (arms I and III); at 4 weeks and at 3, 6, and 12 months after completion of radiotherapy (arms I and III) or chemotherapy (arms II and IV); and then annually for 2-10 years. Patients are followed at months 3, 6, and 12 and then annually thereafter.