The electron-transport characteristics of modulation-doped GaAs-A1xGa1-xAs heterostructures have been measured over a wide range of temperatures using a diverse set of device structures. Short voltage pulses were used to apply a broad range of lateral (parallel to the interface) electric fields and the resulting current-field characteristics were determined using a sampling oscilloscope and x-y recorder. It was observed that the high electron mobility in these structures initially increased as the electric field was increased from zero. The low-field mobility reached a maximum at fields below 500 V/cm and then dropped quickly at low temperatures for increasingly higher electric fields. At higher temperatures (200 K to 300 K) there was comparatively little change in the mobility for fields up to 2 kV/cm. For higher fields (above 2 kV/cm) it was found that the electrons could gain enough energy to be thermionically emitted over the conduction-band discontinuity from the high-mobility GaAs to the low-mobility A1GaAs. This real-space transfer (RST) of electrons resulted in current saturation or various degrees of negative differential resistance (NDR) in the samples being studied. It was demonstrated that the new real-space transfer mechanism could be used in the creation of fast electron switching and storage devices and also high-frequency oscillators.