Abstract: The delayed fluorescence of 1-amino-4-hydroxy-anthraquinone is observed in the phosphorescence spectrum of dyed nylon-6 fiber. This indicates that energy transfer occurs between polymer (impurity groups) and the dye. Kinetic analysis shows that the critical distance of energy transfer equals 52.0Å, and the rate constant of this process is 290 1·mol^-1·s^-1. It is proved that energy is transferred by a mechanism of long range resonance. After being irradiated, the dyed nylon fiber shows less strength loss than the undyed ones, which means the dye functions as a kind of photostabilizer.