Inclusion Criteria (Patients must meet each of the following criteria to be eligible for participation in the trial):

• Male or female patients ≥ 18 years of age
• Patients must have histologically-confirmed diagnoses of relapsed or refractory hematologic malignancy as specified in the protocol
• Patients must have an ECOG performance status of 0 to 2
• Patients must have adequate renal and liver function as demonstrated by laboratory values performed within 5 days, inclusive, prior to administration of the first dose of AP23573
• Patients must be able to understand and give written informed consent

Exclusion Criteria (Patients meeting any of the following criteria are ineligible for participation in the study):

• Women who are pregnant or lactating
• Patients may not have had cytotoxic chemotherapy or radiotherapy within 14 days prior to study entry
• Patients may not receive any investigational anti-cancer agent while on this study or within 14 days prior to the first dose of AP23573
• Patients with known or suspected hypersensitivity to drugs formulated with polysorbate 80 (Tween) or any other excipient contained in the study drug formulation
• Patients with known Grade 3 or 4 hypersensitivity to macrolide antibiotics (e.g., clarithromycin, erythromycin, azithromycin)
• Patients with significant uncontrolled cardiovascular disease
• Patients with known HIV infection
• Patients with any uncontrolled infection
• Patients receiving immunosuppressive agents other than prescribed corticosteroids
• Patients who have had prior therapy with rapamycin, any rapamycin analog or tacrolimus
• Patients with inadequate recovery from any prior surgical procedure or patients having undergone any major surgical procedure within 14 days prior to the first dose of AP23573
• Patients with any other life-threatening illness or organ system dysfunction which, in the opinion of the Investigator, would either compromise the patient's safety or interfere with evaluation of the safety of the study drug
• Patients with a psychiatric disorder or altered mental status that would preclude understanding of the informed consent process and/or completion of the necessary studies
• Patients with another primary malignancy within the past three years (except for non-melanoma skin cancer and cervical carcinomas in situ)
• Patients with the inability, in the opinion of the Investigator, to comply with the protocol requirements

Drugs and Other Treatments to be Excluded (The following drugs and other treatments are not permitted for patients enrolling in the study, either during or within two weeks prior to the first dose of AP23573, unless otherwise specified):

• Chemotherapeutic agents with the following exception that therapy with nitrosoureas (including generics) cannot be given within six weeks prior to the first dose of AP23573
• Other antineoplastic agents
• Immunotherapy (including vaccines) or biological response modifier therapy
• Systemic hormonal therapy with exceptions as specified in the protocol
• Herbal preparations or related OTC preparations containing herbal ingredients (e.g., St John's Wort)
• Radiotherapy for the primary malignancy
• Any other investigational agent during the course of the trial should be discussed with the Sponsor prior to use