Low grade gliomas are the most common pediatric central nervous system malignancies and can occur in different parts of the brain. Patients who undergo gross total resection, usually those with hemispheric tumors, have an excellent prognosis with surgical resection alone. Patients for whom gross total resection is not achievable have a significant risk of disease progression. Therefore, these patients benefit from adjuvant therapy. Multiple chemotherapy regimens have shown some efficacy in residual tumor, but more than 50% of patients experience recurrences. Radiation has been shown to be an effective therapy in the treatment of these tumors. Because of concerns regarding radiation toxicity especially in young children, and progression despite chemotherapy, novel approaches are needed. This protocol represents an attempt to measure the efficacy and safety of use of pegylated interferon for patients with recurrent, refractory Juvenile Pilocytic Astrocytomas (JPA) or optic pathway gliomas. It provides a different approach to the commonly used treatment modalities. The objectives of this study are to determine the response of children with chemotherapy-refractory progressive JPA or optic pathway gliomas (OPG) to weekly pegylated interferon alpha-2b. The secondary objectives include to better identify the toxicities of weekly pegylated interferon alpha-2b (PEG-Intron™) in pediatric patients with unresectable, refractory, recurrent JPAs or optic pathway gliomas, to evaluate various magnetic resonance imaging techniques for noninvasive monitoring of metabolic and biologic changes in the tumors and to evaluate the quality of life for patients with recurrent, refractory JPAs who receive therapy with pegylated interferon alpha-2b (PEG-Intron™).