Inclusion Criteria:

- Patient must have an original diagnosis confirmed by biopsy* of high-grade glial
tumor, low-grade glial tumor, ependymoma, medulloblastoma, primitive neuro-ectodermal
tumor (PNET), Wilms' tumor, rhabdomyosarcoma, Ewing's sarcoma, osteosarcoma,
retinoblastoma, or miscellaneous poor-prognosis solid tumors. Lymphomas and other
lymphoid malignancies will not be studied in this protocol.

* Brain stem glioma patients who have progressed after radiation therapy do not
require histologic confirmation. Brain stem gliomas are defined as intrinsic tumors
of the pons causing diffuse enlargement. These patients are diagnosed on clinical
and radiographic appearance of the lesion and the biopsy requirement will be waived
for this group.

- Patient must have pathologic or imaging confirmation of tumor progression or
recurrence within 4 weeks prior to enrollment.

- Patient must be ≥ 5 years of age and ≤ 21 years of age at the time of study entry.

- Patient must have a Karnofsky performance status or Lansky* play status ≥ 50

* For purpose of determining performance scores, wheelchair-bound patients will be
considered ambulatory.

- Patient must have an adequate supply of stem cells for transplant harvested prior to
study enrollment, with adequate supply defined as 3 x 106 CD34+ cells/kg for
peripheral blood stem cells (PBSC). Cell mobilization method will be left up to the
treating physician's discretion and may include mobilization growth factor alone or
mobilization after chemotherapy. If patient is unable to mobilize the proper amount
of peripheral stem cells, bone marrow may be harvested as the source of hematopoietic
stem cells. In this instance, 3 x 108 mononuclear cells/kg will be considered
adequate. If necessary, a combination of peripheral stem cells and bone marrow can
be used.

- Prior radiation therapy and/or chemotherapy, including cyclophosphamide, are
permitted.

- Prior anti-angiogenic therapy, including thalidomide and oral cyclophosphamide, is
permitted.

- If on corticosteroids for mass effect and/or edema related to the tumor, patient must
be on a stable dose for at least 2 weeks prior to study entry.

- Patient must have a life expectancy > 2 months.

- Patient must have an adequate bone marrow reserve as defined by:

- Hemoglobin ≥ 9.0 g/dl and

- Platelet count ≥ 30,000/ mm3 (transfusion independent) and

- Peripheral absolute neutrophil count (ANC) ≥ 750/mm3

- Patient must have adequate cardiac function tested within 4 weeks of study enrollment
as defined by:

- Shortening fraction of ≥ 27% by echocardiogram or

- Ejection fraction of ≥ 50% by radionuclide angiogram

- Patient must have adequate pulmonary function tested within 4 weeks of study
enrollment as defined by:

- Pulse oximetry > 94% on room air or O2 by nasal cannula and

- No evidence of dyspnea at rest.

- Patient must have adequate hepatic function as defined by:

- Total bilirubin ≤ 1.5x upper limit of normal (ULN) for age and

- SGOT (AST) or SGPT (ALT) ≤ 2.5 x ULN (SGOT ≤ 4x ULN if on Zantac)

- Patient must have adequate renal function as defined by:

- Serum creatinine < 1.5 mg/dl

- Glomerular filtration rate (GFR), calculated via I-125 iothalamate clearance, 24-hour
creatinine clearance, or Schwartz formula*, ≥ 70 mL/min and ≥ 50 mL/min/1.73 m2 done
within 4 weeks of study entry

* The Schwartz formula is an estimated glomerular filtration rate in children based
upon serum creatinine and height. Height (Ht) should be measured in cm and serum
creatinine (Cr) in mg/dL. Proportionality constant (k) is 0.55 for children and
adolescent girls and 0.7 for adolescent boys aged 13-21. This constant is based upon
a series of evaluations performed by Schwartz. Formula: GFR= (k x Ht)/Cr

- If female of childbearing potential (defined as menstruating or amenorrheic from
previous medical treatments), the following guidelines must be adhered to:

- If enrolled in Arm III of this study, patient must be registered at the Celgene
S.T.E.P.S. ® Program.

- If enrolled in Arm III of this study, patient must be willing to practice birth
control as outlined in the S.T.E.P.S. Program from the beginning of the study until
at least 4 weeks following discontinuation of thalidomide therapy. Two reliable
forms of contraception must be used simultaneously unless continuous abstinence from
heterosexual sexual contact is chosen. Contraceptive methods must include at least
one highly effective method (e.g. oral contraceptive pills, injections, hormonal
patches, IUD, or implants), AND one additional effective barrier method (e.g. latex
condom, diaphragm, cervical cap). If hormonal or IUD contraception is medically
contraindicated, another highly effective method or two barrier methods must be used
at the same time.

- Pregnancy surveillance:

- Patient must have a negative in office pregnancy test sensitive to within 50 mIU/mL
(serum or urine) within 24 hours of beginning thalidomide even if continuous
abstinence is the preferred method of birth control.

- A pregnancy test must be performed weekly during the first 4 weeks of therapy and
repeated monthly for patients with regular menses or every 2 weeks for patients with
irregular menses

- Negative pregnancy tests are valid for only 7 days.

- If irregular bleeding or skipped menses, pregnancy test should be performed and
pregnancy counseling given.

- If pregnancy occurs during treatment, thalidomide must be immediately discontinued.
Any suspected lethal exposure must be reported immediately to Celgene Customer Care
Center at 1-888-423-5346, and the patient referred to an OB/GYN experienced in
reproductive toxicity for further evaluation and counseling.

- Patient (or legally authorized representative) must be able to understand and willing
to sign a written informed consent document.

Exclusion Criteria:

- Patient must not have any active, uncontrolled cardiac, hepatic, renal, or
psychiatric disease defined as ≥ grade 3 based on NCI Common Terminology Criteria for
Adverse Events v4.0 (CTCAE).

- Patient must not be receiving any other investigational agents.

- Patient must not have any active infection or concurrent illness obscuring toxicity
or dangerously altering drug metabolism.

- Patient must not have any thromboembolic event (deep vein thrombosis or pulmonary
embolism) less than 3 weeks prior to enrollment.

- Patient must not have a history of allergic reactions attributed to compounds of
similar chemical or biologic composition to any of the agents used in the study.

- Patient must not be pregnant or breastfeeding.

Inclusion of Women and Minorities

-Both men and women and members of all races and ethnic groups are eligible for this
trial.