We present a new predictive model for off-state breakdown in InAlAs/InGaAs and AlGaAs/InGaAs power high electron mobility transistors (HEMTs). The proposed model suggests that electron tunneling from the gate edge, and not impact ionization, is responsible for off-state breakdown in these devices. The model indicates that the crucial variables in determining the off-state breakdown voltage of power HEMTs are the sheet carrier concentration in the extrinsic gate-drain region, and the gate Schottky barrier height. Other design parameters have only secondary impact on the breakdown voltage for realistic device designs.