Inclusion Criteria:

- Male or female patients age 18 or older

- Patients with PTCL according to World Health Organization (WHO) criteria and have
relapsed or are refractory to at least 1 prior systemic, cytoxic therapy for PTCL.
Patients must have received conventional therapy as a prior therapy. Cutaneous-only
disease is no permitted. Patients must have documented evidence of progressive
disease.

- Tumor biopsy available for central hematopathologic review

- Measurable disease according to the IWG criteria

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

- Female patients who are post menopausal for at least 1 year, surgically sterile, or
agree to practice 2 effective methods of contraception through 30 days after the last
dose of study drug or agree to abstain from heterosexual intercourse.

- Male patients who agree to practice effective barrier contraception through 6 months
after the last dose of alisertib or agree to abstain from heterosexual intercourse

- Suitable venous access

- Voluntary written consent

Exclusion Criteria

- Known central nervous system lymphoma

- Systemic antineoplastic therapy, immunotherapy, investigational agent or radiation
therapy within 4 weeks of first dose of study treatment or concomitant use during
study

- Prior administration of an Aurora A kinase-targeted agent, including alisertib; or
all of the 3 comparator drugs (pralatrexate, or romidepsin or gemcitabine; or known
hypersensitivity)

- History of uncontrolled sleep apnea syndrome or other conditions that could result in
excessive daytime sleepiness

- Cardiac condition as specified in study protocol, including left ventricular ejection
fraction (LVEF) <40%

- Concomitant use of other medicines as specified in study protocol

- Patients with abnormal gastric or bowel function who require continuous treatment
with H2-receptor antagonists or proton pump inhibitors

- Known active infection with human immunodeficiency virus (HIV), hepatitis B virus, or
hepatitis C

- Autologous stem cell transplant less than 3 months prior to enrollment

- Patients who have undergone allogeneic stem cell or organ transplantation any time

- Inadequate blood levels, bone marrow or other organ function as specified in study
protocol

- The patient must have recovered to National Cancer Institute Common Terminology
Criteria for Adverse Events (NCI CTCAE) Grade ≤ 1 toxicity, to patients's baseline
status (except alopecia), or deemed irreversible from the effects of prior cancer
therapy

- Major surgery, serious infection, or infection requiring systemic antibiotic therapy
within 14 days prior to the first dose of study treatment

- Female patients who are breastfeeding or pregnant

- Coexistent second malignancy or history of prior solid organ malignancy within
previous 3 years

- Serious medical or psychiatric illness or laboratory abnormality that could, in the
investigator's opinion, potentially interfere with the completion of treatment
according to the protocol