The experimental investigation on properties of (U1-yPuy)O2+/-x shows a deviation in the ideality for the solid solution. Our results on the unit cell parameter, the electrical conductivity, the specific heat, and, the thermal diffusivity have been analyzed to validate this conclusion. The variations in the properties have been interpreted from this new thermodynamical criterion, and, two transitions in the mechanism of U/Pu substitutions in the mixed oxide have been proposed. They occur for two particular plutonium concentrations: 3.1 and 12.5 at%. New types of clusters (Pu'-VO) or (Pu'-VO-U') are introduced to represent the dominant point defect in the structure of the hypostoichiometric mixed oxide for the MOX fuel compositions. The classical ionic model including the clusters (Pu'-VO-Pu') or (Pu'-VO-Pu) can be dominant only above 15 at% of plutonium, i.e. for FBR fuels.