Inclusion Criteria:

- Age ≥ 18 years with HCT comorbidity index < 3

- Any of the following conditions:

- AML and ALL in 1st complete remission (CR) at high risk of relapse based on
negative prognostic factors (for the definition of high-risk of relapse see
Appendix H).

- AML and ALL in 2nd or subsequent CR

- secondary AML in CR

- Absence of timely and suitable fully HLA matched or one HLA locus mismatched family
or unrelated donor and, at Investigator's discretion, absence of other possible
therapeutic alternatives

- Stable clinical conditions and life expectancy > 3 months

- PS ECOG < or = 2

- Patients, or legal guardians, and donors must sign an informed consent indicating
that they are aware this is a research study and have been told of its possible
benefits and toxic side effects

- Serum creatinine < 1.5 x ULN

- Bilirubin < 1.5 x ULN; transaminases < 3 x ULN

- Left ventricular ejection fraction > 45%

- QTc interval < 450 ms

- DLCO > 50%

Exclusion Criteria:

- Patients with life-threatening condition or complication other than their basic
condition

- Contraindication to haploidentical HCT as defined by the Investigator

- Patients with active CNS disease

- Pregnant or lactation.

Exclusion criteria for HSV-Tk infusion:

- Infections requiring administration of ganciclovir, valganciclovir or acyclovir at
the time of infusion: HSV-Tk cells can be administered after a 24-hour
discontinuation interval of antiviral therapy

- GvHD requiring systemic immunosuppressive therapy

- Ongoing systemic immunosuppressive therapy after haploidentical HCT

- Administration of G-CSF after haploidentical HCT

- CD3+ cells ≥ 100/µl at day of planned experimental infusion after haploidentical HCT

- Any grade 3-4 adverse event related to HSV-Tk infusion or a grade 2 adverse event
that does not resolve to no more than grade 1 before the next infusion

For criteria 2, 3 and 4: HSV-Tk cells can be administered after an adequate patient
wash-out period