• Male/female patients who are at least 18 years of age on the day of signing informed consent with histologically confirmed diagnosis of T-cell Non-Hodgkin lymphoma (TNHL) will be enrolled in this study.

• Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 unless compromised by lymphoma with anticipated benefit from chemotherapy as determined and documented by the investigator.

• Histologically confirmed T-cell Non-Hodgkin lymphoma (T-NHL), including but not limited to:

‣ Peripheral T-cell lymphoma not otherwise specified (PTCL nos)

⁃ Angioimmunoblastic T-cell lymphoma (AITL)

⁃ Anaplastic large-cell lymphoma (ALCL)

⁃ Cutaneous T-cell lymphoma (CTCL), including mycosis fungoides (MF)/sezary syndrome patients for whom multi-agent chemotherapy is indicated

⁃ Transformed mycosis fungoides/Sézary syndrome

⁃ Enteropathy-associated T-cell lymphoma (EATL)

⁃ Subcutaneous panniculitis-like T-cell lymphoma (SCPTCL)

⁃ Hepatosplenic T- cell lymphomas

⁃ Gamma delta T-cell lymphomas

⁃ Adult T-cell lymphoma leukemia (ATLL)

⁃ T-prolymphocytic leukemia with nodal or visceral involvement

• Prior therapy- patients with aggressive T-cell lymphoma may have received one cycle of CHOP, CHOEP or EPOCH before enrollment, if necessary, to control the disease.

• For patients with peripheral T-cell lymphoma (PTCL): At least one measurable target lesion ≥ 1.5 cm

• A female patient is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies:

‣ Not a woman of childbearing potential (WOCBP) as defined in Appendix 4 OR

⁃ A woman of childbearing potential (WOCBP) - see Appendix 4 for definition of WOCBP - must have a negative serum or urine pregnancy test during screening and must agree to follow instructions for using acceptable contraception (Appendix 5) from the time of signing consent, and at least 180 days (6 months) after her final dose of mogamulizumab.

• A male patient must agree to use a contraception as detailed in Appendix 5 of this protocol during the treatment period and for at least at least 180 days (6 months) after her final dose of mogamulizumab and refrain from donating sperm during this period.

• Adequate organ and bone marrow function resulted ≤ 10 days prior to first dose of protocol-indicated treatment unless compromised by disease involvement of bone marrow, spleen, or liver as determined and documented by the investigator.

• Patients previously treated with anti-CD4 antibody or alemtuzumab are eligible provided their CD4+ cell counts are ≥ 200/mm.