Nonradiative multistep energy migration is studied for 3,3′-diethylthiacarbocyanine iodide (DTCI) in uniaxially stretched and unstretched poly(vinyl alcohol) films. The results of fluorescence anisotropy decay measurements were found to be extremely different for unstretched and (stretched) systems. For disordered systems, fast depolarization was observed due to effective energy migration between randomly distributed fluorophores. However, for partly ordered systems, much slower depolarization was found as a result of preferential angular distribution of transition dipole moments of identical fluorophores. These results and properties of energy transport in uniaxially stretched polymer films are analyzed using the technique of Monte-Carlo simulation.