We report the growth and characterization of ternary AlxGa1- xAs nanowires by metalorganic chemical vapor deposition as a function of temperature and V/III ratio. Transmission electron microscopy and energy dispersive X-ray spectroscopy show that, at high temperatures and high V/III ratios, the nanowires form a core-shell structure with higher Al composition in the nanowire core than in the shell. We develop a growth model that takes into account diffusion of reactants and decomposition rates at the nanowire catalyst and stem to describe the compositional difference and the shell growth rate. Utilizing this model, we have successfully grown compositionally uniform Al0.16Ga0.84As nanowires. The ability to rationally tune the composition of ternary alloy nanowires broadens the application range of nanowires by enabling more complex nanowire heterostructures.