Fluorescence depolarization in organized molecular media probed by the fluorophores undergoing an excited-state orientation-dependent irreversible inter conversion is discussed. The effect of the angular dependence of the excited-state interconversion on the order parameters and correlation functions is examined in a systematic way by considering different angular dependence for the interconversion kinetic rate. The expected manifestation of this effect in the time-resolved fluorescence depolarization experiments is discussed on the basis of the synthetic decays for the experiments on membrane vesicles suspension and for variable-angle experiments on macroscopically ordered samples. The main properties of the model and its experimental applications are discussed.