The GaN material parameters relevant to the negative differential resistance (NDR) devices are discussed, and their physical models based on the theoretical predictions and experimental device characteristics are introduced. Gunn diode design criteria were applied to design the GaN NDR diodes. A higher electrical strength of the GaN allowed operation with higher doping (similar to 10(17) cm(-3)) and at a higher bias (90 V for a 3 mu m thick diode). The transient hydrodynamic simulations were used to carry out the harmonic power analysis of the GaN NDR diode oscillators in order to evaluate their large-signal microwave characteristics. The GaAs Gunn diode oscillators were also simulated for a comparison and verification purposes. The dependence of the oscillation frequency and output power on the GaN NDR diode design and operating conditions are reported. It was found that, due to the higher electron velocities and reduced time constants, GaN NDR diodes offered twice the frequency capability of the GaAs Gunn diodes (87 GHz vs. 40 GHz), while their output power density was 2 x 10(5) W/cm(2) compared with similar to 10(3) W/cm(2) for the GaAs devices. The reported improvements in the microwave performance are supported by the high value of the GaN Pf (2)Z figure of merit, which is 50-100 times higher than the GaAs, indicating a strong potential of the GaN for the microwave signal generation.