The application of angle-resolved fluorescence depolarization techniques to the simultaneous determination of the directions of the transition moments and orientational order of dye molecules incorporated into uniaxially stretched polymer films is discussed and illustrated. The directions of the transition moments of pyranine molecules are determined in a general way, on exciting the molecules in two distinct electronic transitions and monitoring the fluorescence emission under the same conditions. This assumes that the fluorescence emission occurs via the same transition moment for every excited absorption band. Experiments on perylene molecules show that the directions of the transition moments can also be determined from measurements utilizing a single electronic absorption band. In this case the orientational distribution of the molecules is assumed to have the form given by the maximum entropy method. Finally, it is shown the directions of the transition moments of DPH molecules in unstretched polymer films can be determined with this technique. It appears that these molecules are oriented to a very small, yet measurable, extent in unstretched films.