Using data from the XMM-Newton and INTEGRAL observatories , we have detected a cutoff at energies above 10 keV in the X-ray spectra of the ultraluminous X-ray sources HoIX X-1 and M82 X-1 . The spectra obtained can be described by a model of Comptonization of radiation in a gas cloud of moderate temperature ( kT \sim 2 –3 keV ) and high optical depth ( \tau \sim 15 –25 ) . Such conditions can be fulfilled during supercritical accretion of matter onto a stellar-mass black hole accompanied by a strong gas outflow . The results of this work confirm the existence of a spectral state specific to ultraluminous X-ray sources , which is unlike any of the known spectral states in normal X-ray binaries . \englishkeywords black holes , accretion , Comptonization , ultraluminous X-ray sources