Inclusion Criteria:

          -  Patients must be older than 3 years and less than or equal to 25 years of age at the
             time of enrollment

          -  Patients with neurofibromatosis are eligible

          -  Histologic confirmation is not required for this if the patient has neurofibromatosis
             type 1 (NF-1) with MRI findings consistent with optic pathway glioma or JPA. Any other
             tumors will need histological confirmation, either at the time of diagnosis or at the
             time of recurrence. The histological diagnosis includes World Health Organization
             (WHO) grade I JPA

          -  Patients must have measurable residual disease, defined as tumor that is measurable in
             two or three perpendicular diameters on MRI. For a lesion to be considered measurable,
             it must be at least twice the slice thickness on MRI (i.e visible on more than one
             slice)

          -  All patients must have a brain MRI with and without contrast (gadolinium) within 30
             days prior to study enrollment. All patients with history of spinal or leptomeningeal
             disease and those patients with symptoms suspicious of spinal disease, must have a
             spine MRI with contrast (gadolinium) performed within 30 days prior to study
             enrollment. Lumbar puncture is necessary if there is evidence of tumor dissemination
             on the MRI of spine

          -  Performance Level: Karnofsky > or equal to 50% for patients > 10 years of age or
             Lansky > or equal to 50 for patients < 10 years of age

          -  Patients must have recovered (to CTC v.5.0 ≤ Grade 1 unless indicated below) from the
             acute toxic effects of all prior chemotherapy, immunotherapy prior to entering this
             study, with the exception of alopecia, weight changes and Grade I or II lymphopenia

               -  Must not have received myelosuppressive chemotherapy within 3 weeks of enrollment
                  onto this study (6 weeks if prior nitrosourea)

               -  At least 7 days must have elapsed since the completion of therapy with other
                  biologic agents. For other biologic agents that have known adverse events
                  occurring beyond 7 days after administration, this period must be extended beyond
                  the time during which adverse events are known to occur

               -  At least 3 half-lives of the antibody after the last dose of a monoclonal
                  antibody. Specifically for bevacizumab 36 days after the last dose

               -  At least 3 weeks from the last surgical resection, prior to start study drug

               -  At least 42 days after the completion of any type of immunotherapy, e.g. tumor
                  vaccines

               -  Patients must have had their last fraction of cranial or craniospinal Radiation ≥
                  24 months prior to study entry

               -  Patients who have received polyinosinic-polycytidylic
                  acid-polylysine-carboxymethylcellulose (Poly-ICLC) are eligible for this trial if
                  all acute Poly-ICLC -related toxicity has resolved

               -  Patients must not have received Pegylated interferon previously

          -  Must not have received growth factor within 2 weeks of entry into this study

          -  Patients who are receiving corticosteroids must be on a stable or decreasing dose for
             at least 1 week prior enrollment in the study

          -  Adequate organ, hematological, renal, and pulmonary function

          -  If history of depression or psychiatric illness, has to be well controlled with
             antidepressants and/or under psychiatrist/psychologist care

        Exclusion Criteria:

          -  Patients who are receiving concurrent chemotherapy, or who are currently receiving
             other investigational chemotherapeutic agents or concurrently receiving radiation

          -  Patients with a known hypersensitivity to interferon-alpha

          -  Prior use of Pegylated interferon or interferon

          -  Less than 2 years since completion of radiation therapy

          -  Pregnant or breast-feeding females are excluded

          -  Patients with clinically significant unrelated systemic illness

          -  Dental braces or prosthesis that interferes with magnetic resonance (MR) imaging

          -  History of noncompliance to medical regimens

          -  Patients unwilling to or unable to comply with the protocol

          -  Patients with a positive history of Hepatitis B or Hepatitis C

          -  Male patient whose sexual partner(s) are women of childbearing potential who are not
             willing to use adequate contraception, during the study and for 8 weeks after the end
             of treatment

          -  Patients should not receive immunization with attenuated live vaccines within one week
             of study entry or during study period

          -  Patient with diagnosis of Diffuse Intrinsic Pontine Glioma