SIRADs (self-indicating instant radiation alert dosimeters) are designed to measure accident radiation doses. As the energy of radiation is usually unknown in such situations, a detector with a weak energy dependence of its response to dose would be ideal. We have studied the energy dependence of the dose response of SIRADs in the range from 50kVp to 10MV, which corresponds to photon equivalent energies from 25.5keV to 2.2MeV. The response to the same dose at 25.5keV is (29+/-4)%(+/-1s) lower than the response at 1.4MeV. The response to a dose slowly increases with radiation energy. This energy dependence is relatively weak in comparison with the dependence for radiographic films and similar in magnitude to the dependence for lithium fluoride thermoluminescence dosimeters. This energy dependence of the response diminishes the accuracy of dose assessments in radiation fields of unknown energy, but does not significantly compromise the core ability of the devices to provide visual estimates of radiation doses.