||Ultrafast mechanisms of radiation detection in granular YBaCuO films are studied in the wide wavelength range from millimeter waves to near infrared. With an increase in radiation frequency, the Josephson detection at the grain-boundary weak links is replaced by electron heating into the grains. This change occurs in the submillimeter wavelength range. The electron-phonon relaxation time tau /sub eph/ is determined from direct measurements, quasi-stationary electron heating measurements, and the frequency dependence of the current at which maximum voltage shift is observed. The temperature dependence of tau /sub eph/ at T<or=40 K was found to be tau /sub eph/ approximately T/sup -1/. The results show that detectors with a response time of a few picoseconds at nitrogen temperature are attainable.