The following criteria is provided for health care professionals.

Inclusion Criteria:

Phase I: Patients must have histologically confirmed relapsed or refractory Non-Hodgkin's lymphoma, Hodgkin's Disease or multiple myeloma (defined by World Health Organization (WHO) criteria).

Phase II: Patients must have histologically confirmed relapsed or refractory T-Cell Lymphoma (as defined by WHO criteria).

• Must have received first line chemotherapy. No upper limit for the number of prior therapies
• Evaluable Disease
• Age ≥18 years
• Eastern Cooperative Oncology Group (ECOG) performance status ≤2
• Patients must have adequate organ and marrow function as defined in the protocol
• Adequate Contraception
• Ability to understand and the willingness to sign a written informed consent document.
• Inclusion Criteria for Multiple Myeloma patients specified in the protocol.

Exclusion Criteria:

• Prior Therapy
  • Exposure to chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier.
  • Systemic steroids that have not been stabilized to the equivalent of ≤10 mg/day prednisone prior to the start of the study drugs.
  • No other investigational agents are allowed.
• Central nervous system metastases, including lymphomatous meningitis
• History of allergic reactions to Pralatrexate or Romidepsin.
• Uncontrolled intercurrent illness
• Pregnant women
• Nursing women
• Current malignancy or history of a prior malignancy, as outlined in the protocol.
• Patient known to be Human Immunodeficiency Virus (HIV)-positive
• Active Hepatitis A, Hepatitis B, or Hepatitis C infection