The use of substances capable of inhibiting one or more enzymes of the histone deacetylase family (histone deacetylase inhibitors) for the therapeutic treatment of Philadelphia-negative myeloproliferative syndromes (polycythemia vera, essential thrombocythemia or idiopathic myelofibrosis) is described. The dosage of the above-mentioned substances is significantly lower than that normally used for the care of other tumor syndromes and may be from 10 to 150 mg/day/patient.