Background: * Tumors of the thymus are rare and can be treated with surgery, but it is often difficult to determine whether a thymic tumor is malignant based on biopsy alone and the long-term survival rate is less than 50 percent. Because thymic tumors are so rare, most treatment knowledge comes from a relatively small series of cases, and the choice of treatment usually depends on the hospital or clinic staff's experience and familiarity with a given chemotherapy and surgery regimen. * Belinostat is an investigational anticancer drug that has not yet been approved by the Food and Drug Administration for use in any cancer. Researchers are interested in determining whether belinostat can be combined with conventional chemotherapy to safely and effectively treat advanced thymic cancer. Objectives: * To determine a safe and tolerable dose of belinostat that can be given in combination with cisplatin, doxorubicin, and cyclophosphamide. * To determine if belinostat (combined with the abovementioned standard chemotherapy regimen) is effective against thymic cancer cells. Eligibility: \- Individuals at least 18 years of age who have been diagnosed with advanced or recurrent thymic malignancy that is not considered to be curable with surgery or radiation therapy, and who have not received previous chemotherapy treatment. Design: * Participants will be screened with a physical exam, blood tests, and imaging studies as directed by the study researchers. * Participants will receive six 21-day cycles (18 weeks) of treatment with belinostat in combination with cisplatin, doxorubicin, and cyclophosphamide. The treatment will require continuous infusion over 3 days, and participants will remain in the treatment center during this time. Participants will have regular blood tests, clinic visits, and imaging studies during the treatment period. * Participants who complete the six treatment cycles with no severe side effects may be offered the option to continue treatment with belinostat alone. * After the 18-week study period, participants will return for regular follow-up exams for at least 4 weeks, and will be asked to remain in contact with the study researchers once a year to continue to study long-term effects....

Background: * New options for the treatment of patients with advanced thymoma and thymic carcinoma are needed. * Belinostat, N-hydroxy-3-(phenylsulphamoylphenyl) acrylamide, is a hydroxamic acid deacetylase inhibitor that is able to inhibit both histone deacetylase inhibitors (HDAC) Class I and II enzymes. * An ongoing phase II study of belinostat in recurrent or metastatic thymic malignancies has shown activity which warrants further consideration of belinostat in the first line. * Belinostat alterations in target protein levels due to gene expression changes may allow increased sensitivity of cancer cells to conventional chemotherapy. Objectives: Primary Objectives * In the Phase I portion the primary objective will be to determine a safe and tolerable phase 2 dose, dose limiting toxicities (DLTs) and preliminary activity for the combination of belinostat by continuous intravenous (IV) infusion (CIVI) with cisplatin, doxorubicin and cyclophosphamide in patients with advanced thymic malignancies. * In the Phase II portion the primary objective will be to determine the clinical response rate (partial response (PR)+complete response (CR)) of belinostat in combination with cisplatin, doxorubicin and cyclophosphamide in the first line treatment of patients with advanced thymic malignancies. Secondary Objectives * To determine time to response, duration of response, progression free survival (PFS) and overall survival (OS). * To determine the toxicity profile and safety of this combination. * To assess exploratory correlative markers in relation to response to treatment (immunohistochemistry and array Comparative Genomic Hybridization (CGH)) Eligibility: * Patients with histologically confirmed advanced thymic malignancies who are chemotherapy na(SqrRoot) ve. * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Adequate renal, hepatic and hematopoietic function Design: * The Phase I portion of the study will consist of four dose levels and dose escalations will follow according to traditional 3 patient cohorts. * Once the maximum tolerated doe is determined, the phase II portion of the study will begin. * Belinostat will be given as a 48h CIVI starting on day 1, doxorubicin as a slow intravenous (IV) injection on days 2 and 3, cisplatin will be infused over 1 hour on day 2 and cyclophosphamide as a slow IV infusion on Day 3. * Treatment will be given every 21 days for no more than 6 cycles or until disease progression. Treatment with belinostat alone may continue until disease progression.