The University of California at Santa Barbara free‐electron laser was used to investigate the kinetics of electrons bound to shallow donors in n‐GaAs by saturation spectroscopy. The resonant photothermal conductivity arising from 1s–2p+ shallow donor excitations in a magnetic field was measured at intensities greatly exceeding that of earlier investigations and saturation of bound‐to‐free photoionization transitions was achieved. The impurity resonance photoconductive signal shows a distinct intensity dependence caused by competing bound‐to‐free transitions which saturate differently. This permits a more detailed evaluation of the electron recombination kinetics than was previously possible, yielding the ionization probability of the 2p+ state, the transition time of electrons from the 2p+ level to the gound state, and the recombination time of free carriers.