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). (this has to be numbered)
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.