This work deals with photoenhanced currents in organic materials within the long-wavelength range of absorption outside the singlet-exciton absorption range. The influence of both photon and triplet exciton-trapped charge interactions on these currents is considered. The analysis has revealed that for low electric field and thick samples the spectrum of photoenhanced current reflects the triplet-exciton absorption spectrum, whereas for high electric field and thin samples the photocurrent spectrum does not correspond to this spectrum. The proposed model of photon detrapping of charge carriers from macrotraps with a certain thermalization length enables to explain the experimentally observed decrease of photoenhanced current with the decrease of photon energy.