The curative principle behind allogeneic hematopoietic stem cell transplantation (HSCT) is eradication of the malignant cells of the patient (recipient) by donor graft cells, a process termed graft-versus-leukemia (GVL) effect. GVL is traditionally mediated by donor αβ T cells in an immunological process driven by genetical differences between individuals, i.e. an allogeneic response. For this reason, αβ T cells also cause an unwanted and dangerous complication of HSCT called graft-versus-host disease (GVHD) in which healthy recipient cells are targeted by donor cells with great risk of morbidity and mortality to the patient. In addition to αβ T cells, other cells from the donor stem cell graft, termed innate effector lymphocytes, can contribute to the GVL effect. These are termed natural killer (NK) cells and T-cell receptor (TCR) γδ cells, the latter being a subset of T cells. NK and TCR γδ cells can recognize and eliminate leukemic cells in a direct tumor response independent of conventional allogeneicity. Therefore, opposite αβ T cells, innate effector lymphocytes cells can mediate GVL but are not likely to cause GVHD. The main indications for HSCT in adults are acute myeloid leukemia (AML) and myelodysplastic syndrome (MDS). Approximately 50% of AML/MDS transplant patients experience significant acute GVHD and 30% experience relapse of the malignant disease. Prospective clinical studies from the research group of the investigators have shown that patients with high doses of innate lymphocytes in stem cell grafts and during early immune reconstitution after HSCT have a reduced risk of both GVHD and relapse. The aim of this clinical trial is therefore to administer innate donor lymphocyte infusion (iDLI) enriched in NK and TCR γδ cells and depleted of αβ T cells in patients early after HSCT. By improving the HSCT procedure with iDLI cell therapy the scope is less GVHD and less relapse of the malignant disease and thereby improved survival and life quality in AML/MDS patients.