RATIONALE: Interferon-alfa may interfere with the growth of cancer cells. Giving interferon-alfa following chemotherapy and peripheral stem cell transplantation may be an effective treatment for Hodgkin's disease or non-Hodgkin's lymphoma.

PURPOSE: Randomized phase III trial to determine the effectiveness of interferon alfa-2b following chemotherapy and stem cell transplantation in treating patients who have recurrent or refractory Hodgkin's disease or non-Hodgkin's lymphoma.

OBJECTIVES: I. Determine the efficacy of interferon alfa-2b in reducing the relapse rate in patients with recurrent or refractory Hodgkin's disease or non-Hodgkin's lymphoma in second remission following high dose chemotherapy and autologous stem cell transplantation. II. Compare the time to disease progression and survival in this patient population treated with interferon alfa-2b vs no further treatment. III. Assess the tolerability of these treatment regimens in these patients.

OUTLINE: This is a randomized, multicenter study. Patients are stratified according to lymphoma subtype. Patients are randomized to one of two treatment arms. Arm I: Patients receive no further therapy following high dose chemotherapy and autologous stem cell transplantation. Arm II: Beginning 4 weeks after high dose chemotherapy and autologous stem cell transplantation, patients receive interferon alfa-2b subcutaneously three times a week. Treatment continues for 18 months in the absence of disease progression or unacceptable toxicity. Patients are followed every 6 months until disease progression.

PROJECTED ACCRUAL: A total of 360 patients (180 per treatment arm) will be accrued for this study within 4-5 years.

DISEASE CHARACTERISTICS: Histologically proven non-Hodgkin's lymphoma or Hodgkin's disease Diffuse small cell (i.e., chronic lymphocytic leukemia, small lymphocytic, immunocytoma) Follicular Mantle cell Peripheral T cell Diffuse large B cell Leukemic (i.e., lymphoblastic, Burkitt's) First relapse or first progression after responding to a salvage regimen and high dose chemotherapy with autologous stem cell transplantation (second remission) Response of greater than 50% of tumor mass decrease observed at time of progression Prior high dose chemotherapy plus autologous stem cell transplantation as first line therapy allowed

PATIENT CHARACTERISTICS: Age: 18 to 64 Performance status: ECOG 0-2 Life expectancy: Not specified Hematopoietic: Not specified Hepatic: Bilirubin no greater than 1.5 mg/dL Transaminase no greater than 3.0 times upper limit of normal Renal: Creatinine no greater than 1.7 mg/dL Other: Not pregnant or nursing Fertile patients must use effective contraception No other prior or concurrent malignancies except curatively treated (by radiotherapy or surgery) basal cell skin cancer or carcinoma in situ

PRIOR CONCURRENT THERAPY: Biologic therapy: See Disease Characteristics No other concurrent immunotherapy No concurrent hematopoietic growth factors Chemotherapy: See Disease Characteristics No concurrent chemotherapy Endocrine therapy: Not specified Radiotherapy: No concurrent radiotherapy Surgery: Not specified