‣ a) Pathologically-confirmed mature T-cell lymphomas at the enrolling institution.

‣ Permitted histologies include (for dose escalation and expansion):

‣ i) Stage ≥Ib CTCL, which has relapsed or progressed after at least two systemic therapies. In order to ensure balanced enrollment for patients with systemic T-cell lymphoma and CTCL, a maximum of 15 CTCL patients will be enrolled in expansion cohort.

‣ ii) Systemic anaplastic large cell lymphoma that has relapsed after therapy containing brentuximab vedotin.

‣ iii) T-cell prolymphocytic leukemia (treatment naïve permitted)

‣ For the following histologies, patients are required to have received at least 1 prior therapy (dose escalation and expansion):

‣ iv) T-cell large granular lymphocytic leukemia

‣ v) Aggressive NK-cell leukemia

‣ vi) Adult T-cell leukemia/lymphoma

‣ vii) Extranodal NK/T- cell lymphoma, nasal type

‣ viii) Enteropathy-associated T-cell lymphoma

‣ ix) Monomorphic epitheliotropic intestinal t-cell lymphoma

‣ x) Hepatosplenic T cell lymphoma

‣ xi) Subcutaneous panniculitis-like T-cell lymphoma

‣ xii) Primary cutaneous anaplastic large cell lymphoma

‣ xiii) Primary cutaneous gamma/delta T-cell lymphoma

‣ xiv) Primary cutaneous CD8-positive aggressive epidermotropic cytotoxic T-cell lymphoma

‣ xv) Peripheral T-cell lymphoma, not otherwise specified

‣ xvi) Angioimmunoblastic T cell lymphoma

‣ xvii) Follicular T-cell lymphoma

‣ xviii) Nodal peripheral T-cell lymphoma wih T follicular helper phenotype

‣ b) Nodal periphal T-cell lymphoma wih T follicular helper phenotype Specific for T-PLL and TFH lymphoma expansion: histologies must be pathologically confirmed at the enrolling institutions i) T-cell prolymphocytic leukemia (treatment naïve permitted) ii) T-follicular helper lymphomas (must have received at least 1 prior treatment)

‣ c) Age ≥18 years at time of enrollment

‣ d) Performance status, as assessed in the ECOG grading system, ≤2

‣ e) Laboratory criteria.

‣ Laboratory criteria

‣ i) For dose escalation phase:

⁃ Absolute neutrophil count ≥1.0 K/mcL (Note: growth factor is allowed)

⁃ Platelet count ≥80 K/μl or ≥50 K/μl if due to lymphoma

⁃ Creatinine ≤1.5 × ULN OR Measured calculated creatinine clearance ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN

‣ i. Creatinine clearance should be calculated per institutional standard

‣ d. Direct bilirubin ≤1.5x upper limit of normal (ULN) or ≤3x ULN if documented hepatic involvement with lymphoma, or ≤5x ULN if history of Gilbert's syndrome; AST and ALT ≤ 3x ULN; or ≤ 5x ULN if due to lymphoma involvement

‣ ii) For dose expansion phase:

⁃ Absolute neutrophil count ≥1.0 K/mcL or ≥0.5 K/mcL if due to lymphoma or ≥0.0 K/mcL if due to T-PLL or large granular lymphocytic leukemia (LGL) (Note: growth factor is allowed).

⁃ Platelet count ≥80 K/μl or ≥50 K/μl if due to lymphoma

⁃ c. Creatinine ≤1.5 × ULN OR Measured calculated creatinine clearance ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN

‣ i. Creatinine clearance should be calculated per institutional standard d. Direct bilirubin ≤1.5x upper limit of normal (ULN) or ≤3x ULN if documented hepatic involvement with lymphoma, or ≤5x ULN if history of Gilbert's syndrome; AST and ALT ≤ 3x ULN; or ≤ 5x ULN if due to lymphoma involvement

‣ f) Measurable disease, defined by at least one of the following:

• Revised International Working Group Classification for systemic lymphoma19

• Atypical T lymphocytes quantifiable by flow cytometry or morphology in the peripheral blood or bone marrow

• mSWAT (Modified Severity Weighted Assessment Tool) \>0

• g) Ability to swallow pills

• h) Women of reproductive potential\* must have a negative serum or urine β human chorionic gonadotropin (βhCG) pregnancy test within 14 days of initiating therapy. All women of reproductive potential and all sexually active male patients must agree to use adequate methods of birth control (e.g. latex condoms) throughout the study and for 3 months after the last dose of study drug.

⁃ A woman of reproductive potential is a sexually-mature woman who: has not undergone a hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in the preceding 24 consecutive months).

• The effects of duvelisib on conception, pregnancy, and lactation are unknown. Since duvelisib has not been evaluated in pregnant or nursing women, the treatment of pregnant women or women of childbearing potential who are not using a highly effective contraception is contraindicated.