Gallium Nitride (GaN) transistors present an opportunity in power electronics to achieve excellent performance. However, GaN devices still face challenges before they are widely used due to the technology maturity. The switching speed of GaN devices is extremely fast in power electronics applications. The large dv/dt and di/dt can couple with parasitic parameters in the device and the power loop, which can lead to unintended high frequency oscillations and stability problems in GaN-based circuits. The oscillations of voltage and current are easily happened, especially in bridge structure, which make it difficult for high frequency application. The purpose of this paper is to study this behavior based on the negative conductance oscillator theory and double pulse test circuit is chosen to study the stability of GaN-based bridge circuit. A negative conductance oscillator model is constructed to analyze this behavior based on negative conductance oscillator theory. The accuracy of the model is verified by a simulation study and experiment involving Hybrid Drain-embedded Gate Injection Transistor (HDGIT).