Inclusion Criteria  Patients aged ≥ 18 years at time of screening Written informed consent by the patient or the patients' legally authorized representative prior to screening  Patients with histologically or cytologically confirmed diagnosis of one of the following subtypes of T-cell lymphoma:  Peripheral T-cell lymphoma (PTCL): Angioimmunoblastic T-cell lymphoma (AITL), PTCL, not otherwise specified (PTCL-NOS), nodal PTCL with T-follicular helper (TFH) and follicular T-cell lymphoma (FTCL) Cutaneous T-cell lymphoma (CTCL) (stages II-B, III, and IV): Mycosis fungoides (MF) and Sezary syndrome (SS) Patients must have received at least 2 prior systemic therapies. Patients with PTCL must have at least 1 measurable lesion Patients with CTCL must have assessable disease by response criteria for CTCL (Olsen EA, 2011) Eastern Cooperative Oncology Group Performance Status (ECOG PS) = 0-2 Life expectancy of at least 3 months Adequate bone marrow, renal and hepatic functions  Exclusion Criteria:  Patients with central nervous system (CNS) involvement Patients with Adult T-cell leukemia/lymphoma (ATLL) Prior allogeneic stem cell transplant Prior treatment with ONO-4685, anti-PD-1, anti-PD-L1, anticytotoxic T lymphocyte associated protein 4 (CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways Patients with malignancies (other than T-cell lymphoma) except for completely resected basal cell carcinoma, stage I squamous cell carcinoma, carcinoma in situ, or any other malignancies that has not relapsed for at least 2 years History of severe allergy or hypersensitivity to any monoclonal antibodies, other therapeutic proteins or corticosteroid (e.g., dexamethasone) History of infection with Mycobacterium tuberculosis within 2 years prior to the first dose of study treatment Patients with systemic and active infection including human immunodeficiency virus (HIV), hepatitis B or C virus infection Patients not recovered to Grade 1 or stabilized from the adverse effects (excluding alopecia) of any prior therapy for their malignancies Women who are pregnant or lactating