Inclusion Criteria:

• Histologic or cytogenetic documented diagnosis of T-ALL or T-LBL.
• Disease that is refractory to at least one prior chemotherapy regimen, or has relapsed following complete remission to at least one prior chemotherapy regimen.
• At least 4 weeks since the last dose of prior last chemotherapy, or radiotherapy before beginning treatment with 506U78 (2 weeks is permitted if growth of blast cells is significant).
• Adequate function of other organ systems as measured as follows.Serum creatinine is less than 1.5 times of upper limit of normal and estimated creatinine clearance >=50 mL/min. Hepatic transaminases (SGPT and SGOT) <=3 x upper limit of normal, bilirubin is less than 1.5 times of upper limit of normal(<=5 x upper limit of normal if it is related by T-ALL or T-LBL).
• Adequate performance status (ECOG-PS<=2).
• Capable of giving informed consent which includes compliance with the requirements and restrictions listed in the consent form.
• Patient is willing to accept hospitalization during the blood sampling for pharmacokinetic measurement (i.e., Cohort 1: for pharmacokinetic sample collection during both cycle 1 and 2; and Cohort 2: for pharmacokinetic sample collection during cycle 1).
• Female subjects who are of child-bearing potential must have a negative pregnancy test at the Screening Visit and agree to utilize contraceptive methods during participation in the study and for at least six months following the last dose of 506U78 Injection. Female subjects may be defined as of non-child-bearing potential if they are physiologically incapable of becoming pregnant, including any female who is post-menopausal. For purposes of this study, postmenopausal is defined as one year without menses.

Exclusion Criteria:

• Active infection at time of treatment.
• Concurrent disease or condition that would make the subject inappropriate for study participation.
• Receiving any other anticancer agents or enrolled on any investigational study during the course of the study.
• Patients must have recovered to Grade I or less toxicity of all previous chemotherapy prior to treatment.
• History of seizure disorder within one year prior to the date of informed consent.
• Pregnancy (as demonstrated by a positive pregnancy test at pre-study/screening) or breastfeeding. Fertile women and men must practice adequate contraception throughout the study and at least 6 month after the last dose of study drug.