A Study to Test the Safety and Efficacy of Erlotinib Plus Bevacizumab to Treat Advanced Thymoma and Thymic Cancer

Inclusion Criteria: * Histologically confirmed invasive, recurrent or metastatic thymoma or thymic carcinoma not amenable to potentially curative therapy by surgery in the opinion of the investigator. Original biopsy of tumor is sufficient for diagnoses unless otherwise clinically indicated. * Patients must have measurable disease per RECIST. Note: Any scans or x-rays used to document measurable disease must be obtained within 28 days prior to registration. * Patients must have had prior chemotherapy (no limit for prior regimens) for metastatic disease. * Patients must not have had any form of systemic anticancer therapy within 21 days prior to being registered for protocol therapy. * Patients receiving radiation therapy must have completed their radiation at least 21 days prior to being registered for protocol therapy, and toxicities due to radiation must have recovered to ≤ grade 1 or baseline prior to registration. Previously radiated area(s) must not be the only site of disease. * Be at least 18 years of age at the time of consent. * Patient's must have laboratory data as specified below within 14 days of registration to study: 1. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 times upper limit of normal (ULN) (unless liver metastases are present, in which case AST/ALT ≤ 5 times upper limit of normal will be acceptable). 2. Total bilirubin ≤ 1.5 mg/dl. 3. White blood cell (WBC) count \> 3000/mm3 4. Absolute neutrophil count (ANC) ≥ 1500/mm3 5. Platelets ≥ 100,000/mm3 6. International normalized ration (INR) of prothrombin time ≤ 1.2, and aPTT no more than 5 seconds longer than the ULN 7. Urine protein:creatinine ratio 1.0 at screening. * Patients must not have prior history of malignancy in the past 5 years with the exception of basal cell and squamous cell carcinoma of the skin. Other cancers with low potential for metastasis, such as in situ cancers (e.g., Grade 1, TA TCC (low grade superficial bladder cancer), colonic polyp with focus of adenocarcinoma) can also be enrolled after approval from the study chair. * No prior use of an EGFR inhibitor or anti-angiogenic agent. * No use of an investigational agent within 30 days prior to registration for study protocol. * Must not have any contraindications to the use of erlotinib or bevacizumab as per the package labeling for either product. * No uncontrolled hypertension ( e.g. \> 150/100 mmHg pretreatment) * No history of unstable angina. * No history of New York Heart Association (NYHA) Grade II or greater congestive heart failure * No history of myocardial infarction or angina pectoris/ anginal equivalent in the last 6 months (the patient may be on anti-anginal medications if the symptoms have been entirely controlled for greater than 6 months )within 6 months prior to registration for protocol therapy. * No history of stroke within 6 months prior to registration for protocol therapy. * No clinically significant peripheral vascular disease. * No evidence of bleeding diathesis or coagulopathy.(Low dose anticoagulant therapy to maintain patency of a vascular access device is allowed). * Patients must not have been using aspirin (\>325 mg/day) or another nonsteroidal anti-inflammatory medications known to inhibit platelet function daily within 10 days prior to registration.. * Patients may not be taking the following drugs known to inhibit platelet function: dipyridamole (Persantine), ticlopidine (Ticlid), clopidogrel (Plavix) and cilostazol (Pletal). * No known evidence of central nervous system involvement or brain metastases. If symptomatic must be confirmed by Head CT or Brain MRI within 6 weeks prior to being registered for protocol therapy. * No major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to registration for protocol therapy. * No anticipation of need for major surgical procedure during the course of the study. * No minor surgical procedures such as fine needle aspirations or core biopsies within 7 days prior to registration for protocol therapy. * No history of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to registration for protocol therapy. * No serious, non-healing wound, ulcer, or bone fracture. * No history of hemoptysis. * No history of deep vein thrombosis or pulmonary embolism. * No active infections.