Inclusion Criteria:

1. Patients must have histologically or cytologically confirmed low or intermediate grade neuroendocrine carcinoma. Patients with neuroendocrine tumors associated with MEN1 syndrome will be eligible.
2. Patients must have at least one measurable site of disease according to RECIST that has not been previously irradiated. If the patient has had previous radiation to the target lesion(s), there must be evidence of progression in the lesion(s) since the radiation.
3. Patients must have at least one lesion suitable for perfusion CT. The lesion should be greater than or equal to 3 cm in size in the cranial caudal direction.
4. Patients who are on a somatostatin analogue must be on a stable dose (no change in mg dose of long acting octreotide or lanreotide, changes in dosing interval of +/- 1 week is allowed) for 2 months prior to date of randomization.
5. Prior radiation therapy is permitted. A recovery period of at least 4 weeks after completion of radiotherapy is required prior to date of randomization.
6. Patients may have received prior interferon or cytotoxic chemotherapy. There are no limitations on the number of prior regimens. Patients who had no prior therapy are eligible. At least 28 days must have elapsed since last treatment.
7. Patients may have received prior therapy targeting c-kit, abl, PDGFR, or EGFR (imatinib, gefitinib, erlotinib, cetuximab).
8. Age >/= 18 years of age, because no dosing or adverse event data are currently available on the use of bevacizumab and everolimus in patients < 18 years of age.
9. Patients must have unresectable or metastatic disease.
10. Zubrod performance status of 0 or 1.
11. Patients must have adequate organ and marrow function as defined below: Leukocytes >/= 3,000/mcL; absolute neutrophil count >/=1,500/mcL; platelets >/=120,000 /mcL; total bilirubin </=1.5 times the institutional upper limit of normal (ULN); AST(SGOT)/ALT(SGPT) </=3.0 times institutional ULN (</= 5 X ULN in patients with liver metastases); creatinine </= 2.0 OR, creatinine clearance >/= 60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal
12. Patients not on anticoagulation must have PT/PTT within 1.2 X the upper limit of normal.
13. Patients on full-dose anticoagulation (warfarin or low molecular weight heparin) are eligible provided that both of the following criteria are met: The patient has an in-range INR (between 2 and 3) on a stable (no change in the prior 2 weeks) dose of oral anticoagulant or on a stable (no change in the prior 2 weeks) dose of low molecular weight heparin. The patient has no active bleeding or known pathological condition that carries a high risk of bleeding such as varices.
14. Patients must have resting blood pressure (BP) no greater than 140 mmHg (systolic) or 90 mmHg (diastolic) for eligibility. Initiation or adjustment of BP medication is permitted prior to date of randomization.
15. Women of child-bearing potential must have a negative urine pregnancy test within 7 days prior to date of randomization. Women who have had menses within the past 2 years, who have not had a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy are considered to be of child-bearing potential.
16. Ability to understand and the willingness to sign a written informed consent document and ability to comply with study and/or follow-up procedures.
17. Men and women of reproductive potential must use effective means of contraception. Oral, implantable, or injectable contraceptives may be affected by cytochrome P450 interactions, and are therefore not considered effective for this study. Barrier method of contraception is required during the study. Contraception should continue for 6 months after the last dose of bevacizumab.

Exclusion Criteria:

1. Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study.
2. Prior treatment with a mTOR inhibitor or bevacizumab.
3. Chronic treatment with systemic steroids or another immunosuppressive agent.
4. A known history of immunocompromise, including a positive HIV test. An HIV test will not be required; however, previous medical history will be reviewed.
5. Inadequately controlled hypertension (defined as systolic blood pressure >140 and/or diastolic blood pressure > 90 mmHg on antihypertensive medications).
6. Any prior history of hypertensive crisis or hypertensive encephalopathy.
7. New York Heart Association (NYHA) Grade II or greater congestive heart failure.
8. History of myocardial infarction or unstable angina within 6 months prior to date of randomization.
9. History of stroke or transient ischemic attack within 6 months prior to date of randomization.
10. Known history of brain or leptomeningeal metastases.
11. Significant vascular disease (e.g., aortic aneurysm, aortic dissection).
12. Symptomatic peripheral vascular disease.
13. Evidence of bleeding diathesis or coagulopathy.
14. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to date of randomization or anticipation of need for major surgical procedure during the course of the study.
15. Minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to date of randomization.
16. History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to date of randomization.
17. Serious, non-healing wound, ulcer, or bone fracture.
18. Proteinuria at screening as demonstrated by either: urine protein:creatinine (UPC) ratio >/= 1.0 at screening, OR, Urinalysis for proteinuria >/= 2+ (patients discovered to have>/= 2+ proteinuria on urinalysis at baseline should undergo a 24 hour urine collection and must demonstrate </= 1g of protein in 24 hours to be eligible).
19. Known hypersensitivity to any component of bevacizumab.
20. Pregnant or lactating. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately.