Fluorescence quenching of dye molecules such as coumarin 153, DCM and nile red by the stable 2,4,6-tri-tertbutylphenoxyl radical in an MTHF glass matrix at 77 K was studied by means of subnanosecond time-resolved fluorescence spectroscopy. The quenching process is ascribed to the dipole-dipole interaction amenable to Forster theory. The average critical energy transfer distances were determined to be 20, 27 and 31 Angstrom for coumarin 153, DCM and nile red, respectively. These values are consistent with those evaluated from spectroscopic data.