Inclusion Criteria:

1. Patients with haematological malignancies, according to WHO classification, such as:

   • acute myeloid leukaemia -AML- in CR1 except "low-risk cases" defined by t(15;17), t(8;21), inv 16 or normal cytogenetics at diagnosis with FLT3-ITD negative and NPM-1 positive, with no high risk clinical criteria
   • any AML beyond CR1
   • acute lymphoblast leukaemia -ALL- in CR1 only if at "high risk" defined by cytogenetics as t(9;22), t(4;11) or for persistence of minimal residual disease (MRD)
   • any ALL beyond CR1
   • chronic myeloid leukaemia -CML- in chronic phase (CP) or accelerated phase (AP) intolerant/not responsive to TK-inhibitors
   • myeloproliferative disorders -MPD-
   • myelodysplastic syndrome -MDS- with intermediate or high risk International Prognostic Scoring System (IPSS)
   • diffuse large cell lymphoma -DLCL- with a chemosensitive relapse or beyond CR1
   • lymphoblastic and Burkitt lymphoma with a chemosensitive relapse or beyond CR1
   • mantle cell lymphoma -MCL- with a chemosensitive relapse or beyond CR1
   • follicular lymphoma -FCL- with a chemosensitive relapse or beyond CR2
   • Hodgkin lymphoma -HD- with a chemosensitive relapse or beyond CR1
   • chronic lymphocytic leukaemia -CLL- at "poor risk" in CR1 or with a chemosensitive relapse
   • CLL relapsing after high dose chemotherapy
   • T-cell non Hodgkin lymphoma -T-NHL- in CR1 or beyond
   • multiple myeloma -MM- at high risk for cytogenetics or ISS stage 3 in CR1 following high dose chemotherapy
   • MM at any relapse/progression except refractory disease

2. Availability of an HLA-identical sibling donor (MRD) or HLA-identical unrelated donor (MUD)

   • HLA-identity defined by the following markers: A, B, DRB1, DQB1 or a single or double Cord Blood unit (CB) with at least a 4 out of 6 HLA-matching by the following markers: A, B and DRB.

   A) identity between the 2 CB units and the recipient;

   B) Two identical CB units with one or two mismatches with the recipient;

   C) Two CB units with one mismatch between them and two mismatches with the recipient. We will prefer mismatches either for class I or for class II antigens; we will avoid mismatches concerning both classes I and II together.

3. Target graft size (unmanipulated, preferably not cryopreserved)

   • bone marrow: 2 to 10 x 106 CD34+ cells/kg BW recipient or > 2 x 108 nucleated cells/kg BW recipient or
   • peripheral blood: 4 to 10 x 106 CD34+ cells/kg BW recipient
4. Age > 18 and < 70 years
5. Karnofsky Index > 80 %
6. Adequate contraception in female patients of child-bearing potential
7. Written informed consent

Exclusion Criteria:

1. Secondary malignancies
2. Previous allogeneic transplantation
3. Hematopoietic cell transplantation-specific comorbidity index > 4 (HCT-CI Sorror et al, Appendix M)
4. Known and manifested malignant involvement of the CNS
5. Active infectious disease
6. HIV- positivity or active hepatitis infection
7. Impaired liver function (Bilirubin > upper normal limit; Transaminases > 3.0 x upper normal limit)
8. Impaired renal function (Creatinine-clearance < 60 ml/min; Serum Creatinine > 1.5 x upper normal limit).
9. Pleural effusion or ascites > 1.0 L
10. Pregnancy or lactation
11. Known hypersensitivity to treosulfan and/or fludarabine
12. Participation in another experimental drug trial within 4 weeks before day -6
13. Non-co-operative behaviour or non-compliance
14. Psychiatric diseases or conditions that might impair the ability to give informed consent