We invert high spectral resolution hard X‐ray observations of the 1980 June 27 solar flare to obtain the parent X‐ray‐producing electron population. Assuming that collisions are the dominant loss mechanism, the accelerated electron population is derived as a function of time through the flare, using a continuity equation. We find that there appear to be two separate components in the accelerated electrons: an impulsive component with a spectrum peaked at 50 keV, and a slowly varying component with a power‐law spectrum extending down to 20 keV. ©1996 American Institute of Physics.