The goal of this clinical research study is to learn if treatment with two types of chemotherapy combinations can help to control peripheral T-cell lymphoma.

All of the drugs used in this study are commonly used in the treatment of cancer. However, using these drugs in combination is investigational.

During treatment, you will be given two different cycles of chemotherapy, which will be alternated every 21 days.

For Cycle 1, cyclophosphamide will be given by vein two times a day on Days 1,2, and 3. Each dose will take around 3 hours to give. Mesna will be given by vein nonstop over Days 1 through 3. Pegylated liposomal doxorubicin will be given by vein over 1 hour on Day 2. Vincristine will be given by vein on Days 4 and 11. Dexamethasone will be given by mouth on Days 1 through 4 and 11 through 14. Other drugs will be given before, during, and after chemotherapy to help decrease the risk of developing side effects. These drugs may be given by mouth or by injection.

For Cycle 2, methotrexate will be given by vein over 2 hours on Day 1 and over 22 hours on day 1. Cytarabine will be given by vein twice a day on Days 2 and 3. Each dose will take about 2 hours to give. Other drugs will be given before, during, and after treatment to help decrease the risk of developing side effects. These drugs may be given by mouth or by injection.

To help increase the blood counts and help decrease the risk of developing infections, your doctor may decide that treatment with filgrastim is necessary. Filgrastim may be given as once-a-day injections under the skin starting 24 hours after the end of Day 4 vincristine (Cycle 1) and starting 24 hours after the end of Cytarabine (Cycle 2). Your blood counts will be monitored and filgrastim is stopped when the levels become normal.

Cycles 1 and 2 will be alternated every 21 days. Both Cycles 1 and 2 can be given on an outpatient basis if your physician authorizes it. However, if your serum creatinine (blood test) reaches a certain level, Cycle 2 should be given on an inpatient basis.

Depending on how the disease responds, treatment may be stopped after 2,4, or 6 cycles. However, treatment may continue for up to 8 cycles.

During treatment, you will have around 2-3 tablespoons of blood collected at least once a week for routine tests.

After every 2 cycles, tumors will be measured using x-rays or other scans (CT, MRI, etc.) and bone marrow samples will be taken. Heart scans or heart function tests may also be needed if you doctor feels it is necessary.

If the disease gets worse or you experience any intolerable side effects, you will be taken off the study and your doctor will discuss other treatment options with you.

After the last cycle of chemotherapy, you will have follow-up exams scheduled. During these exams, you will have a chest x-ray and CT scans of the chest, abdomen (stomach) and pelvis (waist area), and PET scan. You will have blood collected (2-3 tablespoons) for routine tests. If your doctor feels it is necessary, you may also have a sample of bone marrow collected. You may choose to have long-term follow-up exams at M. D. Anderson or with your local physician.

This is an investigational study. All of the study drugs are approved by the FDA for cancer treatment and are commercially available. However, the use of the drugs in combination is experimental. Up to 55 participants will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

1. Confirmed diagnosis of previously untreated T-cell Non Hodgkin's Lymphomas and NK lymphomas, with the exception of cluster of differentiation antigen 30 (CD30+) alk1+ T-anaplastic large cell lymphoma (ALCL). Patients with skin involvement alone are also excluded. For patients with skin involvement as part of systemic disease, prior topical treatment only is allowed.
2. Patients with a performance status of 3 or less (Zubrod Scale - see Appendix D).
3. Serum bilirubin </= 1.5 mg/dl and serum creatinine </= 2.0 mg/dl unless due to lymphoma; Absolute neutrophil count (ANC) >/= 1000 mm^3 and platelets >/= 100,000 mm^3 unless due to lymphoma.
4. Cardiac ejection fraction 50% or greater by multigated radionuclide angiography (MUGA) or echocardiogram.
5. Ages 18 and older.
6. Patients must be willing to receive transfusions of blood products.

Exclusion Criteria:

1. Patients with CD30+ alk1+ T-anaplastic large cell lymphoma (ALCL) or patients with skin involvement alone.
2. Pregnancy
3. HIV positive serology
4. Central nervous system (CNS) involvement
5. Co-morbid medical, such as Child's Class C liver cirrhosis, end-stage renal disease, and symptomatic congestive heart failure, or psychiatric illnesses that preclude treatment with intense dose chemotherapy as determined by the primary investigator
6. Concurrent or previous malignancy whose prognosis is poor (<90% probability of survival at 5 years)

Adverse events were assessed from the initiation of the regimen through the end of the chemotherapy cycle, up to 3 years.