This is a phase 1 study of pegylated arginine deiminase (ADI-PEG 20) in pediatric patients who deficient in the expression of tumor argininosuccinate synthetase, and have failed prior treatments. The study hypothesis is that this drug will be safe in pediatric patients.

This phase 1 study will use a classic 3 dose levels by 3 patients per dose level design. Once the maximum tolerated dose is reached, additional patients may be enrolled at that dose level.

Inclusion Criteria:

1. Prior diagnosis of failed current standard treatment(s), or AEs associated with prior systemic agent(s) that resulted in discontinuance of that agent(s).
2. Argininosuccinate synthetase deficient tumor.
3. Measurable disease as assessed by >5% blasts on bone marrow aspirate for patients with leukemia or using RECIST 1.1 criteria for solid tumors.
4. Age 4 to ≤ 18 years.
5. No prior systemic treatment for the tumor in the last 2 weeks for solid tumors and 1 week for leukemia, except hydroxyurea used only to control very high WBC.
6. Fully recovered from any prior surgery and no major surgery within 4 weeks of initiating treatment. Surgery for placement of vascular access devices is acceptable.
7. Female subjects of 10 years and older and male subjects must be asked to use appropriate contraception for both the male and female for the duration of the study.
8. No concurrent investigational studies are allowed.
9. For solid tumor subjects only: Absolute neutrophil count (ANC) >750/µL.
10. For solid tumor subjects only: Platelets >50,000/µL.
11. For solid tumor subjects only: Serum uric acid ≤ 8 mg/dL (with or without medication control).
12. Serum creatinine ≤ 1.5 x the upper limit of normal range, or, if serum creatinine >1.5 x the upper limit of normal range, then the creatinine clearance must be ≥ 60 mL/min.

Exclusion Criteria:

1. Serious infection requiring treatment with systemically administered antibiotics at the time of study entrance.
2. Pregnancy or lactation.
3. Expected non-compliance.
4. Uncontrolled intercurrent illness.
5. Subjects who have had any anticancer treatment prior to entering the study and have not recovered to baseline or ≤ Grade 1 AEs due to agents administered.
6. Subjects who had been treated with ADI-PEG 20 previously.
7. History of seizure disorder not related to underlying cancer.
8. Known HIV positivity.