Patients with cutaneous T cell lymphoma (Mycosis fungoides or Sezary Syndrome) or peripheral T cell lymphoma as defined in #1 who have received any number of prior systemic therapies and who have previously been treated with vorinostat will be included in a third and independent arm. Patients can be enrolled in this arm if they received prior vorinostat and experienced disease progression, subsequent relapse, or had to discontinue to agent due to toxicity.