[en] The removal of long-lived radionuclides, which belong to the so-called minor actinides elements, neptunium, americium and curium, from the high level nuclear wastes separated during the reprocessing of the irradiated nuclear fuels in order to transmute them into short-lived nuclides, can substantially decrease the potential hazards associated with the management of these nuclear wastes. In order to separate minor actinides from high-level liquid wastes (HLLW), a liquid-liquid extraction process was considered, based on the use of diamide molecules, which display the property of being totally burnable, thus they do not generate secondary solid wastes. The main extracting properties of dimethyldibutyltetradecylmalonamide (DMDBTDMA), the diamide selected for the development of the DIAMEX process, are briefly described in this paper. Hot tests of the DIAMEX process (using DMDBTDMA) related to the treatment of an mixed oxide fuels (MOX) type HLLW, were successfully performed. The minor actinide decontamination factors of the HLLW obtained were encouraging. The main results of these tests are presented and discussed in this paper. (authors). 9 refs., 2 figs., 7 tabs