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We present a theoretical model of an AlGaN-GaN high electron mobility field effect transistor (HEMT) that includes a nonlinear model of the strain polarization fields produced at the heterointerface. Recent experimental work has indicated that the macroscopic polarization in III-nitride alloys is a nonlinear function of the material composition. It is well known that the behavior of a GaN-AlGaN HEMT depends greatly upon the properties of the strain-induced polarization fields formed at the GaN-AlGaN heterointerface. It is the purpose of this paper to provide a detailed model of a GaN-AlGaN HEMT that includes a nonlinear formulation of the polarization. The model is found to agree well with recent experimental measurements made for GaN-AlGaN HEMTs when the nonlinear polarization model is included. The cutoff frequency, transconductance, and current-voltage characteristics are computed. The effect of the nonlinear polarization model on the sheet carrier density is also presented.