A new method for characterization of HEMT distortion parameters, which extracts the coefficents of a Taylor series expansion of Ids(Vgs, Vds), including all cross-terms, is developed from low-frequency harmonic measurements. The extracted parameters will be used either in a Volterra series model around a fixed bias point for 3rd-order characterization of small-signal Ids nonlinearity, or in a large-signal model of Ids characteristic, where its partial derivatives are locally characterized up to the 3rd order in the whole bias region, using a novel neural-network representation. The two models are verified by one-tone and two-tone intermodulation distortion (IMD) tests on a PHEMT device