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 the upper limit of normal (ULN); Alanine transaminase (ALT) aspartate transaminase (AST) within two weeks before protocol entry.

9. Patients are required to have adequate renal function as indicated by a serum
creatinine 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.