Inclusion Criteria:

          -  Males and females of 18 years to 80 years of age;

          -  Understand and voluntarily sign an informed consent document prior to any study
             related assessment or procedure;

          -  Patients able to adhere to the study visit schedule and protocol requirements;

          -  Patients with histologically proven, CD30 positive (at least 5% of cells according to
             local examination) peripheral T-cell lymphoma (PTCL) according to the 2016 World
             Health Organization (WHO) classification for whom gemcitabine treatment is expected. A
             biopsy at relapse is highly recommended;

          -  Patients who have evidence of relapsed disease after at least one line (and no more
             than three lines) of treatment or who were refractory to a first or subsequent line of
             treatment;

          -  Patients with Ann Arbor stage I - IV;

          -  Patients with Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 2;

          -  Patients with at least one measurable disease, i.e. one nodal or extra-nodal lesion of
             1.5 cm or more;

          -  Negative pregnancy test for females of childbearing potential (FCBP);

          -  Female patients of child bearing potential must use an effective method of birth
             control (i.e. hormonal contraceptive, intrauterine device, diaphragm with spermicide,
             condom with spermicide or abstinence) during treatment period and 6 months thereafter.

          -  Males must use an effective method of birth control during treatment period and 6
             months thereafter.

        Exclusion Criteria:

          -  Any significant medical condition or laboratory abnormality unrelated to PTCL, or
             psychiatric illness that would prevent the patient from participating in the study and
             from signing the informed consent form;

          -  Any condition that confounds the ability to interpret data from the study;

          -  Other types of lymphomas, e.g. B-cell lymphoma;

          -  Central nervous system and/or meningeal involvement by PTCL;

          -  Signs or symptoms of Progressive Multifocal Leukoencephalopathy;

          -  Preexistent peripheral neuropathy ≥ grade 2, whatever the cause;

          -  Contraindication to any drug contained in the chemotherapy regimen;

          -  Known hypersensitivity to recombinant proteins, murine proteins, or to any excipient
             contained in the drug formulation of brentuximab vedotin;

          -  Subjects with HIV or HTLV1 positivity;

          -  Subjects with active hepatitis B or C. Chronic carriers of hepatitis B without
             hepatitis B virus (HBV) DNA positive blood are eligible. Subjects with non-active
             hepatitis C (with normal transaminases) are eligible;

          -  Chronic or acute, clinically significant, untreated bacterial, viral or fungal
             infection;

          -  Any of the following laboratory abnormalities:

               1. Absolute neutrophil count (ANC) < 1500 cells/mm3 (1.5 x 109/L);

               2. Platelet count <75,000/mm3 (75 x 109/L);

               3. Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≥ 3.0 x
                  upper limit of normal (ULN). AST or ALT may be elevated up to 5 x ULN if their
                  elevation can be ascribed to the presence of hematologic/solid tumor in the
                  liver;

               4. Serum total bilirubin > 1.5 x ULN;

               5. Serum lipase level > 2 x ULN;

               6. Serum creatinine > 2.0 mg/dL and/or creatinine clearance or calculated creatinine
                  clearance < 40 mL/minute;

               7. Hemoglobin < 8g/dL;

          -  Active malignancies other than PTCL requiring systemic treatment;

          -  Previous treatment with brentuximab vedotin;

          -  Previous treatment with gemcitabine;

          -  Pregnant or lactating females or women of childbearing potential not willing to use an
             adequate method of birth control for the duration of the study;

          -  Known history of any of the following cardiovascular conditions:

               1. Myocardial infarction within 2 years of enrollment

               2. New York Heart Association (NYHA) Class III or IV heart failure

               3. Evidence of current uncontrolled cardiovascular conditions, including cardiac
                  arrhythmias, congestive heart failure (CHF), angina, or electrocardiographic
                  evidence of acute ischemia or active conduction system abnormalities

               4. Recent evidence (within 6 months before first dose of study drug) of a
                  left-ventricular ejection fraction <50%

          -  Patients that have not completed any prior treatment chemotherapy and/or other
             investigational agents within at least 5 half-lives of last dose of that prior
             treatment;

          -  Diagnosed or treated for another malignancy within 3 years before the first dose or
             previously diagnosed with another malignancy and have evidence of residual disease.
             Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not
             excluded if they have undergone complete resection.