This study will examine the safety and effectiveness of peginterferon alpha-2b (PEG-Intron) alone and together with thalidomide in patients with gliomas (a type of brain tumor). Gliomas are nourished by blood delivered through blood vessels whose formation is stimulated by substances produced by the tumor itself. Stopping the growth of new vessels can slow or prevent tumor growth. The Food and Drug Administration has approved various interferons for treating several diseases, including melanoma and some leukemias. These drugs block new vessel growth in patients with recurrent tumors, but in high doses they produce serious side effects. Therefore, this study will use a low dose of PEG-Intron given weekly instead of high doses given several times a week. Thalidomide, currently approved to treat leprosy, also blocks development of new blood vessel formation. In a recent study of thalidomide given to 36 patients with gliomas, 4 patients had tumor shrinkage, 12 had stable disease for at least 2 months, and at least 3 had responses to treatment lasting 6 to 14 months.