Inclusion Criteria:

- Patient's age must be greater than (>) 18 months and less than or equal to (≤) 25
years at the time of diagnosis or recurrence.

- Neuroradiographic evidence of a recurrent posterior fossa medulloblastoma or
recurrent CNS germ cell tumor.

- The presence of a histologically confirmed high grade astrocytoma, GBM, rhabdoid
tumor, supratentorial PNET, or pineoblastoma either at the time of diagnosis or
recurrence.

- Patients must be brought to state of minimum residual disease by surgical reduction
and/or chemotherapy and/or radiation therapy or a combination of above prior to
myeloablative chemotherapy and tandem stem cell rescue.

- Documentation of chemotherapy sensitivity is required for enrollment.
Chemotherapy-sensitive tumors are defined as those tumors which have had a reduction
of 50% after 2-4 cycles of chemotherapy (CTX or platinum). For patients with no
evidence of disease post resection, continued complete remission after 2-4 cycles of
chemotherapy defines chemosensitivity.

- Adequate physiologic function, defined as follows:

- creatinine clearance > 70 ml/minutes/1.73 m2.

- SGPT < 10 x normal and bilirubin < 10 mg/dl.

- Adequate complete blood count (CBC): hemoglobin > 10 gm/dl, absolute neutrophil
count (ANC) > 1500/ul, and platelets > 100,000/ul.

- Informed consent. The patient and/or the patient's legally authorized guardian must
acknowledge in writing that consent to become a study subject has been obtained, in
accordance with institutional policies provided by the United States (U.S.)
Department of Health and Human Services.

- Protocol approval. Approval for the use of this institution's Human Rights Committee
must be obtained in accordance with the institutional assurance policies of the U. S.
Department of Health and Human Services.

- Patients with high-risk medulloblastoma after initial surgery.

- To allow non-English speaking patients to participate in this study, bilingual health
care services will be provided in the appropriate language.

Exclusion Criteria:

- Patients with brain stem glioma are ineligible.