We observe for the first time negative differential resistance (NDR) at room temperature in GaInP/GaAs double-heterojunction bipolar transistors (DHBT's). Both the common-emitter and common-base current-voltage characteristics and their magnetic field dependence have been studied to confirm that the observed NDR is due to resonant tunneling. The collector-base voltages at which the collector current resonances occur are calculated and are consistent with the measured values. We also note that these devices exhibit a low off set voltage of 57 mV and a low saturation voltage of less-than-or-equal-to 2 V, both of which are the lowest reported values for GaInP/GaAs DHBT's. The collector-base breakdown voltage in these DHBT's is 31 V, and its variation with junction temperature is also measured and described.