Inclusion Criteria:

- Patients with histologically proven supratentorial malignant primary gliomas will be
eligible for this protocol. These include glioblastoma multiforme (GBM), anaplastic
astrocytoma (AA), anaplastic oligodendroglioma (AO), anaplastic mixed
oligoastrocytoma (AMO), or malignant astrocytoma NOS (not otherwise specified).

- Patients must have evaluable or measurable disease and have shown unequivocal
evidence for tumor recurrence or progression by MRI or CT scan. This scan should be
performed within 14 days prior to registration and on a steroid dosage that has been
stable for at least 5 days. If the steroid dose is increased between the date of
imaging and the initiation of treatment, a new 20 baseline MR/CT scan is required.
The same type of scan, i.e., MRI or CT must be used throughout the period of
treatment for tumor measurement.

- Patients having undergone recent resection of recurrent or progressive tumor will be
eligible as long as the following conditions apply:

- They have recovered from the effects of surgery

- Measurable disease following resection of recurrent tumor is not mandated for
eligibility into the study. Patients must have evaluable disease.

- To best assess the extent of residual disease post-operatively, a CT/MRI should be
done no later than 96 hours in the immediate post-operative period or 4-6 weeks
post-operatively. If the 96 hour scan is more than 2 weeks from registration, the
scan needs to be repeated.

- The baseline on-study MR/CT is performed within 14 days of registration and on a
steroid dosage that has been stable. If the steroid dose is increased between the
date of imaging and the initiation of Peg-Intron with or without Thalidomide, a new
baseline MR/CT is required on stable steroids for 5 days.

- Patient must have failed prior radiation therapy and must have an interval of greater
than or equal to 4 weeks from the completion of radiation therapy to study entry.

- Patients with prior therapy that included interstitial brachytherapy or stereotactic
radiosurgery must have confirmation of true progressive disease rather than radiation
necrosis based upon either PET or Thallium scanning, MR spectroscopy or surgical
documentation of disease.

- Prior therapy. There are no limitations to number of prior therapies.

- All patients must sign an informed consent indicating that they are aware of the
investigational nature of this study.

- Patients must be > 18 years old, and with a life expectancy > 8 weeks.

- Patients must have a Karnofsky performance status of > 60.

- Patients must have recovered from the toxic effects of prior therapy (including
resolution of effects on laboratory values): 2 weeks from any investigational agent,
4 weeks from prior cytotoxic therapy, 2 weeks from vincristine, 6 weeks from
nitrosoureas, 3 weeks from procarbazine administration, and 1 week for non-cytotoxic
agents e.g. tamoxifen, cis- retinoic acid, etc. (radiosensitizer does not count). Any
questions related to the definition of non-cytotoxic agents should be directed to the
PI.

- Patients must have adequate bone marrow function (WBC > 3,000/l, ANC > 1,500 mm3,
platelet count of > 100,000/mm3, and hemoglobin > 10 gm%), adequate liver function
(SGOT and bilirubin < 2 times the upper limit of normal), and adequate renal function
(creatinine < 1.5 mg/dL or creatinine clearance > 60 cc/min) before starting therapy.
These tests must be performed within 14 days prior to registration. Eligibility level
for hemoglobin may be reached by transfusion.

- Patients with a history of any other cancer (except non-melanoma skin cancer or
carcinoma in-situ of the cervix), unless in complete remission and off of all therapy
for that disease for a minimum of 3 years are ineligible.

- This study was designed to include women and minorities, but was not designed to
measure differences of intervention effects. Males and females will be recruited with
no preference to gender. No exclusion to this study will be based on race. Minorities
will actively be recruited to participate.

- Patients must not be pregnant or nursing, and all patients (both men and women) must
be willing to practice birth control for 1 month prior, during and for 4 months after
treatment with thalidomide. It has been proposed that thalidomide may interfere with
hormonal-based contraception, therefore, barrier methods of contraception (i.e.
diaphragm, condom) MUST be used rather than, or in addition to birth control pills.

- No peripheral neuropathy > grade 1.

- No concurrent use of other investigational agents.

Exclusion Criteria:

- Patients must not have:

- Serious active infection

- Disease that will obscure toxicity or dangerously alter drug metabolism

- Serious intercurrent medical illness.

- Significant illness that in the investigator's opinion cannot be adequately
controlled with appropriate therapy or would compromise the patients ability to
tolerate this therapy.

- Patients must not have received prior therapy with Peg-Intron or Thalidomide.

- Concurrent chemotherapy, immunotherapy, or radiotherapy is not permitted.