Inclusion Criteria:

          1. Patients with confirmed CD30-positive DLBCL or grade 3b follicular non-Hodgkin
             lymphoma (NHL).

          2. Patients must have relapsed or refractory disease following:

               1. second-line or greater salvage systemic therapy, or

               2. frontline cytotoxic systemic therapy, for patients who are ineligible for stem
                  cell transplant (SCT).

          3. Age 18 years and older.

          4. Fluorodeoxyglucose (FDG)-avid disease by positron emission tomography (PET).

          5. An Eastern Cooperative Oncology Group (ECOG) performance status score of 0-2.

          6. Acceptable blood test results.

          7. Females of childbearing potential must have a negative pregnancy test result within 7
             days prior to the first dose of study drug.

          8. Females of childbearing potential and males who have partners of childbearing
             potential must agree to use an effective contraceptive method during the study and for
             6 months following the last dose of brentuximab vedotin or 12 months following the
             last dose of rituximab, whichever is later.

          9. Patients must provide written informed consent.

        Exclusion Criteria:

          1. History of another invasive malignancy that has not been in remission for at least 1
             year. (Exceptions are nonmelanoma skin cancer, curatively treated localized prostate
             cancer, ductal carcinoma, and cervical carcinoma or a squamous intraepithelial lesion
             on PAP smear).

          2. History of progressive multifocal leukoencephalopathy (PML).

          3. Cerebral/meningeal disease related to the underlying malignancy, unless definitively
             treated.

          4. Viral, bacterial, or fungal infection within 2 weeks prior to the first dose of
             treatment.

          5. Chemotherapy, radiotherapy, biologics, and/or other antitumor treatment with
             immunotherapy that is not completed 4 weeks prior to first dose of study drug.

          6. Females who are pregnant or breastfeeding.

          7. Known allergy to any study drug or ingredient contained in the drug formulation of any
             of the study drugs.

          8. Known to be positive for hepatitis B. Known to have active hepatitis C infection or on
             antiviral therapy for hepatitis C within the last 6 months.

          9. Known to be positive for human immunodeficiency virus (HIV).

         10. Patients with previous allogeneic stem cell transplant.

         11. Previous treatment with brentuximab vedotin or bendamustine.

         12. Intolerable toxicity to prior rituximab therapy.

         13. Current therapy with other investigational agents.

         14. Lung disease unrelated to underlying malignancy.

         15. History of a stroke or transient ischemic attack, unstable angina, myocardial
             infarction, or cardiac symptoms within 6 months prior to the first dose of treatment.

         16. Congestive heart failure.

         17. Significant peripheral sensory or motor neuropathy at the start of the study.