PROJECTED ACCRUAL: 40 patients will be entered over approximately 10 months. If 4 or more toxic deaths occur in the first 15 patients or 5 or more toxic deaths occur in the first 30 patients, accrual will stop. As of 05/96, asparaginase has been replaced with pegaspargase; 15-25 additional patients will be accrued. As of 01/97, a maximum of 35 patients will be accrued for PEG asparaginase-containing treatment regimen. As of 5/97, this study is open only to patients with anaplastic large cell and T cell large cell lymphoma. Approximately 60-90 patients will be accrued.