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The steady state and time-resolved photoluminescence (PL) spectra of cubic AlxGa1-xN have been measured for 0 < x < 1. The intensity of the room temperature PL increases by an order of magnitude when the AlN content increases from x = 0 to x = 0.95. Additionally, the PL decay slows down with the decrease of temperature and increase of x. These results show that strong localization of carriers on alloy composition fluctuations plays a large role in determining the intensity and temporal evolution of the PL. The activation energy for the localized carriers increases with the increase of x and reaches the value of 55 meV at x = 0.95.