The response of an electron gas in a quasitwo-dimensional conduction channel depends on a characteristic frequency ω0, defined as the ratio of the plasma wave velocity to the channel length. For a short-gate high electron mobility transistor ω0 can be in the terahertz range. We have used a self-consistent hydrodynamic model of the confined electron plasma to show that significant nonlinear effects are present in its response to harmonic signals at microwave frequencies much lower than ω0. We obtain the oscillatory time dependence of the terminal currents and study the interior dynamics of the electron plasma. We find that in certain device parameter ranges the essential nonlinearity in the microwave response may lead to nonlinear hydrodynamic effects, such as shock wave propagation in the conduction channel. When the boundary conditions at the source and drain terminals are asymmetric, the nonlinear plasma oscillations result in a nonzero dc component of the terminal current, which could be measured by using standard microwave circuits. © 1999 American Institute of Physics.