Abstract: Photoresponse of YBa₂Cu₃O_7-δ hot-electron bolometers to modulated near-infrared radiation was studied at a modulation .frequenc y var y ing from 0.2 MHz to 2 GHz. Bolometers were _fabricated from a 50 12 M thick film and had in-plane areas of 10x10 , um 2 . 2x0.2 s um', 1x0.2 p.m', and 0.5x0.2 jim. We found that nonequilibrium phonons cool down more effectively for the bolometers with smaller area. For the smallest bolometer the bolometric component in the response is 10 dB less than for the largest one.