This is a Phase 1, single-arm, open-label, multi-center study designed to determine an effective and well-tolerated dose and schedule of pralatrexate when administered concurrently with vitamin B12 and folic acid supplementation to patients with relapsed or refractory CTCL. The start of study treatment is defined as the initiation of pralatrexate. A patient may begin pralatrexate, provided he/she has methylmalonic acid (MMA) serum concentrations < 200 nmol/L and homocysteine (Hcy) concentrations < 10 μmol/L at screening. If a patient has elevated MMA and/or Hcy concentrations, vitamin supplementation will be initiated at least 10 days prior to pralatrexate initiation. Once the patient is on study, the dosing of vitamin supplementation must adhere to the schedule defined by the protocol. Vitamin supplementation will consist of vitamin BB12
1 mg intramuscular (IM) every (q) 8-10 weeks, and folic acid 1 mg by mouth (PO) once a day (QD).