The energy distribution of gamma photons scattered in double photon Compton scattering is measured experimentally for 0.662-MeV incident gamma photons. The two simultaneously emitted gamma quanta are investigated using a slow-fast coincidence technique. The experimental data on energy distribution do not suffer from inherent energy resolution of the gamma detector and confirm the continuous nature of energy spectra for the emitted photons. The present results are in agreement with the current theory of this higher-order process.