THAT astrocytomas of the cerebellum are among the most benign of all tumors of the brain has been established by a number of studies.1-20 However, most previous investigations have been concerned with the analysis of relatively short postoperative periods. What ultimately happens to these patients after much longer periods of time has not been established in any sizable group of cases. In 1939 Bailey et al2 published a study of 100 cases of tumors of the brain in children. Of these tumors 24 were classified as benign gliomas of the cerebellum (cases 27 to 50), 23 as astrocytomas, and 1 as a polar spongioblastoma. Two of these patients (cases 47 and 48) were not operated upon, and both died. There were two immediate postoperative deaths (cases 45 and 46), and three patients (cases 41, 42 and 49) died months or years later, one (case 42) after the