Terminated due to slow accrual.

Primary Objectives:

1. To evaluate the response rate for patients with T-cell Non-Hodgkin's Lymphoma (NHL)receiving the combination of vorinostat and bortezomib
2. To evaluate the safety and tolerability of the combination of vorinostat and bortezomib in patients with relapsed or refractory T-cell NHL.

Secondary Objectives:

1. To assess overall survival and time to treatment failure in patients with T-cell NHL treated with the combination of vorinostat and bortezomib.
2. Correlative studies will be done to assess the role of vorinostat mediated apoptosis along with bortezomib synergy. Changes in marker expression from baseline to post treatment will be correlated with patient clinical response.

The Study Drugs:

Vorinostat is designed to cause chemical changes in different groups of proteins that are attached to DNA (the genetic material of cells), which may slow the growth of cancer cells or cause the cancer cells to die.

Bortezomib is designed to block a protein that plays a role in cell function and growth. This may cause cancer cells to die.

Study Drug Administration:

If you are found to be eligible to take part in this study, on Days 1-14 of each 21-day study cycle, you will take vorinostat. Vorinostat capsules are taken by mouth, 2 times a day (1 time in the morning and 1 time in the evening). The capsules must be taken with food (within 30 minutes after a meal).

On Days 1, 4, 8, and 11 of all cycles you will receive bortezomib through a needle in your vein. This will take less than 1 minute.

If you begin to experience severe or intolerable side effects, the study drug schedule may be stopped for up to 2 weeks. If the side effects improve, you may be able to begin to receive the study drugs again, with a lower dose of bortezomib. The vorinostat dose will not be changed. If you continue to have severe or intolerable side effects with the lower dose of bortezomib, you will be taken off study.

Study Visits:

On Day 1 of all cycles, the following tests and procedures will be performed:

• You will receive the vorinostat capsules (a 14-day supply for each study cycle) and instructions on how to take the drug. You will be instructed to return any unused vorinostat capsules back to the study staff at the end of each cycle.
• Your medical history will be recorded, including any drugs that you are taking.
• You will be asked about any side effects you may have.
• You will have a physical exam.
• You will have a neurological exam.

On Day 1, 4, 8, and 11 of all cycles, your vital signs will be measured.

On Day 8 of all cycles, blood will be drawn (about 5 teaspoons) for routine tests.

On Day 1 of every other cycle (Cycles 3, 5, 7, and so on), the following tests and procedures will be performed:

• You will have CT scans and/or Positron emission tomography (PET) scans to check the status of the disease.
• Blood (about 5 teaspoons) will be drawn for routine tests and to check the status of the disease.
• If the doctor thinks it is necessary, you may have a bone marrow aspirate and/or biopsy.

You will have computed tomography (CT) scans and/or PET scans, as needed, every 2 cycles (Cycles 2, 4, 6 and so on), to check the status of the disease.

Length of Study:

You will receive the study drugs for up to 6 months (8 cycles). After 6 months (8 cycles) of receiving the study drugs, if the disease has not gotten worse or has become better, you may be able to stay on study and continue receiving the study drugs. The study drugs would continue to be given at the same dose and on the same schedule. The study visits, blood collections, and optional biopsies will also continue on the same schedule.

If the disease gets worse or you develop severe or intolerable side effects at any time, you will be taken off the study drugs.

End-of-Study Visit:

If you go off study treatment for any reason, you will have an end-of-study visit within 4 weeks of your last dose of study drug or before starting a new treatment. At this visit, the following tests and procedures will be performed:

• You will have a physical exam, including a measurement of your vital signs.
• You will have a neurological exam.
• You will be asked how well you are able to perform the normal activities of daily living (performance status evaluation).
• Blood (about 5 teaspoons) will be drawn for routine tests.
• You will have a CT scan and PET scans to check the status of the disease.

Follow-Up Visits:

After you are off study treatment, you will be contacted by phone call every 2 months to check on how you are doing for up to 5 years. These phone calls will last about 5 minutes.

Up to 40 patients will take part in this study. All will be enrolled at M. D. Anderson.

Inclusion Criteria:

1. Patients must have an established diagnosis of relapsed or refractory T-cell NHL Eligible histologies include; Peripheral T-cell lymphoma (unspecified), CD 30 + anaplastic large cell lymphoma ( ALK-1 positive and ALK-1 negative), angioimmunoblastic T-cell lymphoma, angiocentric/nasal type T/NK-cell lymphoma, intestinal T-cell lymphoma, hepatosplenic gamma delta T-cell lymphoma, subcutaneous panniculitic T-cell lymphoma, transformed Mycosis fungoides; All patients must have had at last one prior system regimen (radiation therapy does not qualify as systemic treatment).
2. Patients who are eligible for blood and marrow transplant can receive this treatment to maximal reduction of tumor bulk: A minimum of two cycles of therapy will be given before crossing over to transplant.
3. Patients must have at least one clear-cut bi-dimensionally measurable site by physical exam and/or computed tomography: Baseline measurements of measurable sites and evaluation of evaluable disease must be obtained within four weeks prior to registration of this study.
4. Patient may have had prior radiation therapy for localized disease: Therapy must be completed at last four weeks before the enrollment in the study.
5. Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
6. Patients must be age 18 years old and above.
7. Patients are required to have adequate bone marrow reserve as indicated: Absolute neutrophil count (ANC) >/= 1000/mm^3; Platelets >/= 80,000/mm^3; Hemoglobin >/= 8g/dL; If there is bone marrow involvement by lymphoma then there is no minimum level of counts required; These values must be obtained within two weeks before protocol entry.
8. Patients must have adequate liver function as indicated by:Bilirubin </= 1.5 times the upper limit of normal (ULN); Alanine transaminase (ALT) </= 2 times the (ULN) or aspartate transaminase (AST) </= 2 times the ULN; These values must be obtained within two weeks before protocol entry.
9. Patients are required to have adequate renal function as indicated by a serum creatinine </= 2.5 mg/dL; This value must be obtained within two weeks before protocol entry.
10. Male patients must agree to use an accepted and effective method of contraception for the duration of the study.
11. Female patients must be willing to use two adequate barrier methods of contraception to prevent pregnancy or agree to abstain from heterosexual activity throughout the study or be post menopausal (free from menses > two years or surgically sterilized).
12. Female patients of childbearing potential must have a negative serum pregnancy test (Beta hCG) within 72 hours of receiving the first dose of vorinostat.
13. Patients must have the ability able to give informed consent.

Exclusion Criteria:

1. Patients with: T-cell lymphoma with skin involvement only are excluded if they have no evidence of systemic disease; T-cell prolymphocytic leukemia (T-PLL); T-cell large granular lymphocytic leukemia; Primary cutaneous CD30+ disorders: anaplastic large cell lymphoma and lymphomatoid papulosis
2. Patients with active Hepatitis B and/or Hepatitis C infection.
3. Patients with known HIV infection are excluded: These patients are excluded secondary to potential to target activated T-cells, in a population of patients already at risk for T-cell depletion, would be a contraindication to therapy.
4. Patients with active infections requiring specific anti-infective therapy are not eligible until all signs of infections are resolved.
5. Patients with left ventricular ejection fraction (LVEF) < 45%.
6. Patients with pre-existing cardiovascular disease requiring ongoing treatment. This includes: Congestive heart failure; Severe CAD; Cardiomyopathy; Uncontrolled cardiac arrhythmia; Unstable angina pectoris; Recent MI.
7. Patients with prior exposure to either vorinostat (including other HDAC inhibitors except valproic acid) or bortezomib: Patients who have received valproic acid (VPA) for the treatment of seizures may be enrolled on this study, but must not have received VPA within 30 days of study enrollment.
8. Patients who are pregnant or breast-feeding: Effects of this treatment on the fetus and young children are unknown at this time.
9. Patients who have had an invasive solid tumor malignancy in the past five years except non-melanoma skin cancers or cervical carcinoma in situ or ductal/lobular carcinoma in situ of the breast who is currently without evidence of disease.
10. Patients undergoing anti-neoplastic chemotherapy, radiation, hormonal (excluding contraceptives) or immunotherapy, or investigational medications within the past four weeks. Receipt of systemic corticosteroids within 7 days of study treatment unless patient has been taking a continuous dose of no more than 10 mg/day of prednisone for at least 1 month.
11. Patients with deep vein thrombosis within three months.
12. Patients with lymphoma involvement of the CNS.
13. Patients who have undergone prior allogenic transplantation: Prior autologous transplantation is accepted.
14. Patient with concurrent use of complementary or alternative medicines that would confound the interpretation of toxicities and anti-tumor activity of vorinostat and/or bortezomib.
15. Patient with a history of allergic reaction attributable to compounds containing boron or mannitol.
16. Patients with psychiatric illness and/or social situations that would limit compliance with the study medication and requirements.
17. Patients with grade 2 or more neuropathy.

13 Months