Pulsed current-voltage measurements on modulation-doped GaAs/Al xGa1-xAs heterostructures are presented at electric fields up to 2 kV/cm. At fields between 0.5 and 2.0 kV/cm we observe up to three well-defined avalanche type current jumps as a function of time. These current jumps show hysteresis effects as a function of the electric field. At even higher electric fields the current becomes irregular and we observe chaotic behavior. To explain the current instabilities we assume that at high electric fields electrons are injected into the AlxGa1-xAs layer parallel to the two-dimensional electron gas. The injected electrons subsequently cause avalanche ionization of occupied DX centers in the Al xGa1-xAs layer. Due to this process, a current filament is created with an exceptionally high mobility which is about 2×10 4 cm2/V s at 10 K.