The biexciton Auger dynamics of alloyed Zn1-xCdx Se/ZnS and Zn1-xCdxSe/CdS core/shell nanoparticles are examined. A series of particles with increasing, cadmium mole fractions are prepared by synthesizing ZnSe nanocrystals followed by cation exchange with cadmium oleate. This is followed by the low-temperature deposition of a CdS or ZnS shell to passivate surface traps. The percent composition of cadmium in the core particles is determined from the absotption spectrum upon cation exchange, and the excited-state dynamics are measured using power-dependent transient absorption spectroscopy. The biexciton lifetimes are controlled by Auger, processes, and the results show that Auger recombination is faster for alloys than for either pure ZnSe or pure CdSe. The lifetimes go through a minimurn at a composition that is approximately 10-40% cadmium. This behavior is assigned to partial hole localization at clusters of cadmium atoms in the alloy, which increases Auger rates through the same mechanism that is responsible for the strong size dependence of Auger processes in nanocrystals. The results can be semiquantitatively understood in terms of effective mass calculations of the hole wave functions, on random (Cd,Zn)Se lattices of varying average compositions corresponding to alloyed nanocrystals of this size. We show that the hole wave function gradients (taken to be related to the Auger rates) also go through a maximum at approximately these alloy compositions.