Fluorescence resonance energy transfer (FRET) experiments were carried out on three pairs of donor-acceptor dyes in polymer films in which the donor dyes had absorption maxima in the range of 350-450 nm. Two of the donors, a coumarin dye and a naphthalimide dye covalently bound to polystyrene, gave nonexponential decays in the absence of acceptors. The decay profiles could be fitted to a stretched exponential form with a beta value on the order of 0.9. We developed equations for analyzing donor fluorescence intensity decay profiles for donor-acceptor mixtures in rigid matrices for the case of donors showing relatively small deviations from exponentiality. To test these equations, we calculate values of the Forster radius (R-0(FR)) from the decay profile data and compare these values to the Forster radius R-0(SO) determined by the traditional spectral overlap method. Agreement between these values validates the methodology developed here for the use of such donor dyes in FRET studies of more complex polymer systems.