The aim of the thesis is to improve the understanding of chemical equilibria involved in the actinides(III) and lanthanides(III) extraction in the DIAMEX-SANEX hydrometallurgical process used for spent nuclear fuel treatment. The chemical extraction equilibria have to be better described in order to improve the modeling of extractant properties of this process. The organic phase is composed of a mixture of extractants: a malonamide, the DMDOHEMA, and a dialkylphosphoric acid, the HDEHP, both diluted in an alkane. The extractant mixture DMDOHEMA-HDEHP has a singular behavior compared to the behavior of the individual extractants. There is a synergistic effect during the extraction of Eu(III) and Am(III) in acid medium (about 1 mol/L aqueous nitric acid concentration) and an antagonist effect at low acidity (pH < 1). In order to understand the behavior of this chemical system, molecular speciation was performed using various spectrometry methods (electrospray ionization mass spectrometry, infrared spectroscopy, nuclear magnetic resonance spectrometry, time-resolved laser-induced fluorescence spectroscopy and UV-visible spectroscopy) but also quantum chemistry calculation to optimize geometry of the complexes. These different techniques have shown the existence of mixed complexes, thermodynamically more stable than the unit complexes, explaining the synergistic extraction of metal cations. The existence of an adduct between the two extractants, consuming the free extractants, may explain the antagonistic effect.