This invention relates to the field of the needs of the life and namely to the field of therapy.It has as the subject matter the use of 7β-hydroxycholesteryl 3β-oleate ester (7-β-OHCOE) in the form of a lipid dispersion directly in the tumours in the forms of liposomes in patients suffering forms anaplastic astrocytomas or glioblastomas.From a short clinical assay on patients at a dosis ranging from 0,05 to 3,2 mg per patient a significant reduction of this total tumoral volume has been observed.