Inclusion Criteria:

- Histologically confirmed malignant glioma (phase I)

- Glioblastoma

- Anaplastic astrocytoma

- Anaplastic oligodendroglioma

- Mixed anaplastic oligoastrocytoma

- Histologically confirmed glioblastoma following radiotherapy and temozolomide (phase
II)

- Progressive or recurrent disease after conformal external-beam radiation therapy and
concurrent temozolomide, followed by ≥ 1 adjuvant course of temozolomide

- Measurable disease by MRI within the past 2 weeks

- Tumor tissue form indicating availability of archived tissue from initial resection
at diagnosis of malignant glioma completed and signed by a pathologist

- Karnofsky performance status 60-100%

- ANC ≥ 1,500/mm³

- Platelet count ≥ 100,000/mm³

- Hemoglobin ≥ 9 g/dL

- Total bilirubin normal

- AST and ALT ≤ 2.5 times upper limit of normal

- Creatinine normal OR creatinine clearance ≥ 60 mL/min

- Urine protein: If proteinuria ≥ +2 protein, a protein level should be < 1,000 mg
by a 24-hour urine collection

- Electrolytes (calcium, chloride, magnesium, potassium, phosphorus, sodium) within
institutional normal limits

- Fertile patients must use 2 forms of effective contraception before, during, and for
≥ 12 months (6 months phase II, bevacizumab arm only) after treatment

- Negative pregnancy test

- Not pregnant or nursing

- At least 5 years since prior malignancy except nonmelanoma skin cancer, or carcinoma
in situ of the cervix, breast, or bladder

- Mini Mental State Exam score of ≥ 15

- Must be able to tolerate MRI

- No serious concurrent infection or medical illness that would jeopardize the ability
of the patient to receive the treatment outline in this protocol with reasonable
safety

- No history of allergic reactions attributed to compounds of similar chemical or
biological composition to gamma-secretase inhibitor RO4929097 or bevacizumab

- Must be able to swallow capsules

- No malabsorption syndrome or other condition that would interfere with intestinal
absorption

- No baseline QTcF > 450 msec (male) or QTcF > 470 msec (female)

- Not history of being serologically positive for hepatitis A, B, or C

- No history of cirrhosis

- No uncontrolled hypocalcemia, hypomagnesemia, hyponatremia, or hypokalemia despite
adequate electrolyte supplementation

- No uncontrolled intercurrent illness including, but not limited to, any of the
following:

- Ongoing or active infection

- Symptomatic congestive heart failure

- Unstable angina pectoris

- A history of torsades de pointes or other significant cardiac arrhythmias other
than chronic, stable atrial fibrillation

- Psychiatric illness and/or social situations that would limit compliance with
study requirements

- No serious or non-healing wound, ulcer, or bone fracture

- No history of abdominal fistula, gastrointestinal perforation, or intra-abdominal
abscess within the past 6 months

- No significant vascular disease (e.g., aortic aneurysm requiring surgical repair or
recent peripheral arterial thrombosis) within the past 6 months

- No clinically significant cardiovascular disease, including any of the following:

- Inadequately controlled hypertension (systolic BP > 160 mm Hg and/or diastolic
BP > 90 mm Hg) despite antihypertensive medication

- History of cerebrovascular accident or transient ischemic attack at any time

- Myocardial infarction or unstable angina within the past 12 months

- NYHA grade II-IV congestive heart failure

- Serious and inadequately controlled cardiac arrhythmia

- Significant vascular disease (e.g., aortic aneurysm or history of aortic
dissection)

- Clinically significant peripheral vascular disease

- No evidence of bleeding diathesis or coagulopathy

- No known hypersensitivity to Chinese hamster ovary cell products or other recombinant
human antibodies

- No requirement for antiarrhythmics or other medications known to prolong QTc

- One or 2 prior treatment regimens allowed

- Recovered from severe toxicity of prior therapy

- At least 3 months since prior radiotherapy

- At least 6 weeks since prior nitrosourea

- At least 3 weeks since prior chemotherapy

- At least 4 weeks since prior and no other concurrent investigational agents

- At least 2 weeks since prior non-cytotoxic, FDA-approved agent (e.g., Tarceva
[erlotinib hydrochloride], hydroxychloroquine, bevacizumab, etc.)

- At least 28 days since any prior surgery

- No prior γ-secretase inhibitors and/or bevacizumab

- At least 10 days since prior and no concurrent enzyme-inducing anti-epileptic drug

- No concurrent combination antiretroviral therapy for HIV-positive patients