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This paper presents a nonlinear equivalent circuit model of microwave power GaN high electron-mobility transistors (HEMTs), amenable for integration into commercial harmonic balance or transient simulators. All the steps taken to extract its parameter set are explained, from the extrinsic linear elements up to the intrinsic nonlinear ones. The predictive model capabilities are illustrated with measured and simulated output power and intermodulation-distortion data of a GaN HEMT. The model is then fully validated in a real application environment by comparing experimental and simulated results of output power, power-added efficiency, and nonlinear distortion obtained from a power amplifier.