Inclusion Criteria:

- Histologically confirmed non-Hodgkin Lymphoma including small lymphocytic lymphoma,
lymphoplasmacytic lymphoma, follicular center cell lymphoma, mantle cell lymphoma,
marginal zone lymphoma, diffuse large B cell lymphoma, Burkitt's lymphoma,
lymphoblastic lymphoma, anaplastic large cell lymphoma, nasal NK/T cell lymphoma,
mycosis fungoides/Sezary syndrome, angioimmunoblastic T-cell lymphoma and peripheral
T-cell lymphomas not otherwise specified

- Received 2 or > prior therapies, which may include hematopoietic cell transplant
(HCT)

- Received treatment with a nucleoside analog, or an alkylating agent, an anthracycline
and/or in the case of B cell lymphomas, rituximab

- Resistant disease to 2 regimens or resistant disease to at least 1 regimen after
first relapse

- Bi-dimensionally measurable disease documented within 30 days prior to enrollment.
Bidimensionally measurable disease is defined as:

- A lymph node or tumor mass that can be accurately measured in two
dimensions by CT,MRI, medical photograph (skin or oral lesion), plain X-ray, PET
scan or other conventional technique and a greatest diameter of 1 cm or >; or
palpable lesions with both diameters > 2 cm (lesion measured in 2 largest
perpendicular dimensions in millimeters)

- For the purposes of this protocol, disease should be located in an area of no
prior radiation therapy or a clear progression in an area that was previously
irradiated

- Adequate organ and marrow function obtained < or = to 14 days prior to enrollment as
defined by a(n):

- ANC > or = to 1,000/microliter

- Platelet count > or = to 100,000/microliter, or > or = to 75,000/microliter if
the bone marrow is involved

- Hemoglobin level > or = to 9 g/dL

- Total bilirubin < or = to 1.5 x institutional upper limit of normality (ULN).(If
abnormal, direct bilirubin less than or equal to 1.5 x institutional ULN)

- ALT or AST < or = to 2.5 x institutional ULN (< or = to 5 x institutional ULN if
liver involvement with lymphoma)

- Serum creatinine < or = to 1.5 x institutional ULN

- Zubrod (ECOG) Performance Status of 0 or 1

- Age > than or = to 18 years

- Life expectancy > or = to 3 months as clinically determined by referring physician

- Female patient is either post menopausal, free from menses for > 2 years, surgically
sterilized or willing to use highly effective methods of contraception (i.e., a
condom in conjunction with a diaphragm, or spermicidal jelly; or oral, injectable, or
implanted birth control; or abstinence ) to prevent pregnancy throughout the study,
starting with visit 1

- Female patients of childbearing potential must have a negative serum pregnancy test
(beta-HCG) within 72 hours of enrollment and should not be nursing due to the
potential for congenital abnormalities and of harm to nursing infants due to this
treatment regimen

- Male patient agrees to use an adequate method of contraception (i.e., a condom if
female partner uses a diaphragm, spermicidal jelly; or oral, injectable, or implanted
birth control; or abstinence) for the duration of the study and for 12 weeks after
the last dose

- Patient must be able to swallow capsules

- Signed and dated IRB/ethics committee-approved informed consent before any protocol
specific screening procedures are performed

- Both men and women of all races and ethnic groups are eligible for this trial

Exclusion Criteria:

- Prior investigational therapy within 3 weeks of enrollment. Investigational therapy
is defined as treatment that is not approved for any indication

- CNS metastases, as indicated by clinical symptoms,cerebral edema, requirement for
corticosteroids and/or progressive growth (treated CNS metastases must be stable for
greater than 2 weeks prior to enrollment)

- Active second malignancy that requires treatment or that would interfere with
assessment of response

- Prior malignancy, except for adequately treated basal cell or squamous cell skin
cancer, in situ cervical cancer, or other cancer with < 5 years of documented
disease-free status

- Treatment with the following within the timeframe specified prior to enrollment:

- Chemotherapy, radiotherapy, immunotherapy (active (such as vaccines) or passive
(such as monoclonal antibodies or immunotoxins)) or major surgery < or = to 3
weeks;

- Nitrosourea, or mitomycin < or = to 6 weeks

- Radioimmunotherapy (e.g. Bexxar or Zevalin) < or = to 12 weeks

- Concurrent enzyme-inducing anticonvulsant agents or valproic acid in last 4
weeks

- Prior bortezomib or any other proteasome inhibitor

- Prior vorinostat or any other histone deacetylase inhibitor

- Concurrent systemic corticosteroids (<10 mg/day of prednisone or equivalent for
adrenal insufficiency or acute allergic reactions allowed)

- Uncontrolled current illness including, but not limited to:

- Clinically or laboratory determined active infection

- Clinically limiting congestive heart failure or ejection fraction (EF) <45%

- Clinically unstable angina pectoris (or myocardial infarction within 6 months of
Day 1)

- Clinically significant cardiac arrhythmia

- Limiting pulmonary hypertension

- Pre-existing neuropathy ≥ grade 2

- Patients with pleural effusions, ascites or peripheral edema grade 2 or >

- HIV

- Active viral hepatitis

- Major surgery or significant traumatic injury within 21 days prior to enrollment
(this does not apply to placement of a venous access device)

- Hypersensitivity to any of the components in vorinostat or bortezomib or agents
containing boron or mannitol

- Significant psychiatric illness/social situations that would limit compliance with
study medication and requirements of the study as determined by study MD

- Significant medical illness or abnormal laboratory finding that would, in the
investigator's judgment, increase the subject's risk by participating in this study