The multi-banded fluorescence and laser properties of 11 new amino- and tosylamino derivatives of 2,5-di(phenyl)-1,3,4-oxadiazole and oxadiazole in various solvents at 293 K are reported. All the compounds investigated possess intra-molecular hydrogen quasi-bond (IHB) of 4.6-5.2 kcal mol-1 in the ground state. In the excited state they can undergo protolytic dissociation or intra-molecular photon-initiated transfer of proton and reveal anomalous fluorescence which cannot be explained within the framework of the Kasha and Kasha-Vavilov rules. Depending upon the excitation wavelength, solvent, concentration and pH of the medium, the compounds studied show a single, double, triple or even a four-banded fluorescence, which has not been reported earlier. The nature of multi-banded fluorescence is explained in terms of the possible photochromic processes in excited states. Quantum yields and decay times of the different fluorescence bands are reported. Anomalous dependence of quantum yield upon concentration of the solution is observed. Laser properties of the compounds studied are carefully tested. Laser action based on the fluorescence of the so-called bi-radical molecules is reported. Various possible arrangements of singlet and triplet levels of compounds investigated are discussed. © 2005 Elsevier B.V. All rights reserved.