We develop a model for the high electron mobility transistor (HEMT) in which we include both hot-electron effects and conduction outside the quantum subband system using hydrodynamic-like transport equations. With such a model we can assess the significance of the various physical phenomena involved in the operation of the HEMT. We calculate results with a two-dimensional numerical technique for both steady-state and transient operation. For a 3-µm device at 77 K, we determine a transconductance of 450 mS/mm, a current-switching speed of 6 ps, and a capacitive charging speed of 4 ps/fanout gate which corresponds to the performance measured by other workers. We also see that electronic heating, velocity overshoot, and conduction outside the quantum well are significant near the pinchoff point. We conclude that the advantage of HEMT is twofold. The excellent conduction in the quantum well results in a low access resistance, and the low impurity concentration in the GaAs results in optimum overshoot effects.