Inclusion Criteria:

- Histologically confirmed new diagnosis of Stage II, III and IV peripheral T-cell NHL
not otherwise specified (NOS), anaplastic large cell lymphoma (ALK negative) (ALK
positive if international prognostic index [IPI] 3, 4, or 5), angioimmunoblastic
T-cell lymphoma, enteropathy associated T-cell lymphoma, hepatosplenic gamma delta
T-cell lymphoma

- Pathology material (hematoxylin and eosin [H&E] stain, immunohistochemistry [IHC] and
pathology report from initial diagnosis, if slides are not available, then 8
unstained slides of 4 micron thickness or a representative block should be sent) will
be reviewed, and the diagnosis confirmed by University Nebraska Medical Center (UNMC)
pathology department (retrospective diagnostic review: treatment may commence prior
to the UNMC review)

- No prior therapy with the exception of prior radiation therapy and 1 cycle of
chemotherapy based on current diagnosis and clinical condition

- Age 19 years or older (the age of consent in Nebraska); age 18 years or older
(applicable to states where the age of majority is 18)

- Expected survival duration of >= six months

- Karnofsky Performance Status >= 70

- Absolute neutrophil count (ANC) >= 1000 cells/mm^3, unless due to lymphoma
involvement of the bone marrow

- Platelet Count >= 100 mm^3, unless due to lymphoma involvement of the bone marrow

- Total bilirubin =< 1.5 x upper normal limit (ULN), or =< 3 x ULN if documented
hepatic involvement with lymphoma, or =< 5 x ULN if history of Gilbert's Disease

- Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN (=<
5 x ULN if documented hepatic involvement with lymphoma)

- Serum potassium within normal range

- Serum creatinine < 2.0 mg/dL or calculated creatinine clearance (CrCl) > 45 mL/min

- Prothrombin time (PT) or international normalized ratio (INR), and partial
thromboplastin time (PTT) =< 1.5 x ULN unless patient is receiving anticoagulants; if
patient is on anticoagulation therapy, levels should be within therapeutic range

- Patients with measurable disease; patients with non-measurable but evaluable disease
may be eligible after discussion with the principal investigator (PI); baseline
measurements and evaluations must be obtained within 6 weeks of registration to the
study; abnormal positron emission tomography (PET) scans will not constitute
evaluable disease, unless verified by computed tomography (CT) scan or other
appropriate imaging

- Patients with measurable disease must have at least one objective measurable disease
parameter; a clearly defined, bidimensionally measurable defect or mass measuring at
least 2 cm in diameter on a CT scan will constitute measurable disease; proof of
lymphoma in the liver is required by a confirmation biopsy

- Women must not be pregnant or breast-feeding due to teratogenic effects of
chemotherapy

- All females of childbearing potential must have a blood test within 2 weeks
prior to registration to rule out pregnancy

- Pregnancy testing is not required for post-menopausal or surgically sterilized
women

- Male and female patients of reproductive potential must agree follow accepted birth
control measures

- Patient must be able to adhere to the study visit schedule and other protocol
requirements

- Patients must be willing to give written informed consent, and sign an
institutionally approved consent form before performance of any study-related
procedure not part of normal medical care; with the exception of 1 cycle of
chemotherapy based on current diagnosis and clinical condition, with the
understanding that consent may be withdrawn by the subject at any time without
prejudice to future medical care

- No serious disease or condition that, in the opinion of the investigator, would
compromise the patient's ability to participate in the study

Exclusion Criteria:

- Pregnant or breast feeding females

- Known positive for human immunodeficiency virus (HIV), human T-lymphotropic virus
type 1 (HTLV-1), or infectious hepatitis, type A, B or C or active hepatitis

- Major surgery within 2 weeks of study drug administration

- Prior malignancies within the past 3 years with exception of adequately treated basal
cell, squamous cell skin cancer, or thyroid cancer; carcinoma in situ of the cervix
or breast; prostate cancer of Gleason Grade 6 or less with stable prostate-specific
antigen (PSA) levels

- Patients with a diagnosis of other peripheral T-cell lymphoma (PTCL) histologies
other than those specified in the inclusion criteria

- Contraindication to any of the required concomitant drugs or supportive treatments,
including hypersensitivity to all anticoagulation and antiplatelet options, antiviral
drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment

- Any other clinically significant medical disease or condition laboratory abnormality
or psychiatric illness that, in the Investigator's opinion, may interfere with
protocol adherence or a subject's ability to give informed consent

- Concomitant administration of nonsteroidal anti-inflammatory drugs (NSAIDs) and
trimethoprim/sulfamethoxazole will not be allowed, since these may result in delayed
clearance of pralatrexate