A model is proposed for the description of the current instabilities in GaAs‐AlGaAs heterojunctions. It consists of three parts: the injection of electrons via the contact into the AlGaAs layer, the partial capture of these electrons in deep centers, and the change with time of the band structure. This last ingredient is crucial, since due to the increase of the total number of electrons in the AlGaAs layer the band bending decreases making real‐space transfer from the AlGaAs layer to the two‐dimensional electron gas possible. We have performed quasistationary simulations of the time dependence of the current. The velocities, average energies, capture rates, etc. were taken from Monte Carlo simulations. It turned out, that the parameters for the modeling of the contact, which are to a high degree unknown, play an essential role. ©1996 American Institute of Physics.