We study electron transport in the alloys of aluminum nitride and gallium nitride and alloys of indium nitride and gallium nitride. In particular, employing Monte Carlo simulations we determine the velocity-field characteristics associated with these alloys for various alloy compositions. We also determine the dependence of the low-field mobility on the alloy composition. We find that while the low-field mobility is a strong function of the alloy composition, the peak and saturation drift velocities exhibit a more mild dependence. Transient electron transport is also considered. We find that the velocity overshoot characteristic is a strong function of the alloy composition. The device implications of these results are discussed.