The myelodysplastic syndromes (MDSs) are a heterogeneous group of clonal haematological diseases characterized by ineffective haematopoiesis and predisposition to acute myeloid leukaemia (AML). The pathophysiology of MDSs remains unclear. A definition of the molecular biology of MDSs may lead to a better classification, new prognosis indicators and new treatments. We studied a series of 40 MDS/AML samples by high‐density array‐comparative genome hybridization (aCGH). The genome of MDSs displayed a few alterations that can point to candidate genes, which potentially regulate histone modifications and WNT pathways (e.g. ASXL1, ASXL2, UTX, CXXC4, CXXC5, TET2, TET3). To validate some of these candidates we studied the sequence of ASXL1. We found mutations in the ASXL1 gene in four out of 35 MDS patients (11%). To extend these results we searched for mutations of ASXL1 in a series of chronic myelomonocytic leukaemias, a disease classified as MDS/Myeloproliferative disorder, and found mutations in 17 out of 39 patients (43%). These results show that ASXL1 might play the role of a tumour suppressor in myeloid malignancies.