We report the design and demonstration of a novel resonant tunneling device which displays bistability in operating current over a range of applied voltages. The device is based on an InAs/AlxGa1−xSb double barrier heterostructure. Although similar in design to conventional resonant tunneling structures, the type‐II InAs/AlxGa1−xSb heterostructure permits the simultaneous accumulation of electrons and holes in the quantum well/barrier region under an applied bias. The steady‐state free‐charge distribution, and hence the device current, is strongly dependent upon the bias history of the device. This effect is manifested as a current‐controlled (S‐shaped) negative differential resistance under conditions in which the device current is specified while the device voltage is measured; a bistable (hysteretic) characteristic is observed under conditions in which the voltage is specified and the current is measured. We have observed current bistability for AlxGa1−xSb barrier compositions in the range 0.4