The use of substances capable of inhibiting one or more enzymes of the histonedeacetylase family (histonedeacetylase inhibitors) for the therapeutic treatment of Philadelphia-negativemyeloproliferative syndromes (polycythemia vera,essential thrombocythemia or idiopathic myelofibrosis) is described. Thedosage of the above-mentioned substances is significantlylower than that normally used for the care of other tumour syndromes and maybe from 10 to 150 mg/day/patient.