We present a comprehensive study of the transport dynamics of electrons in the ternary compounds, Al Ga 1 N and In Ga 1 N. Calculations are made using a nonparabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab initio band models. The effects of alloy scattering on the electron transport physics are examined. The steadystate velocity field curves and low field mobilities are calculated for representative compositions of these alloys at different temperatures and ionized impurity concentrations. A field dependent mobility model is provided for both ternary compounds AlGaN and InGaN. The parameters for the low and high field mobility models for these ternary compounds are extracted and presented. The mobility models can be employed in simulations of devices that incorporate the ternary III-nitrides.Index Terms-Monte Carlo method, semiconductor materials, wide bandgap semiconductors.