The nature of electronic energy transfer in strain-free mounted anthracene-doped naphthalene single crystals at frequencies near that of the (0.0) a-exciton in naphthalene was probed using sensitized resonant two-photon fluorescence excitation (TPE) and second harmonic generation (SHG) spectroscopies. The naphthalene-to-anthracene TPE intensity ratios were found to be 1.2 and 1.6, for excitation of the zero-phonon transition at 1.6 K and 20 K, respectively. This result is consistent with coherent exciton-polariton electronic energy transfer at liquid helium temperatures, and incoherent transfer at high temperatures. Energy transfer for the pure and the anthracene-doped naphthalene systems under investigation was determined to be in the capture limited regime, that is, the trapping event occurs on a timescale which is long compared to the migration of the excitation to the trap. The polariton trapping event is discussed in terms of scattering off a trap with subsequent trapping (i.e., capture) and scattering off a trap without subsequent trapping (i.e., trap scattering). The branching ratio for the trap scattering frequency to the capture frequency, (gamma)(,sc)/(gamma)(,tr), was derived and was calculated to be 5 to 1 for the doped system. The branching ratio was used to determine the individual scattering frequencies: (gamma)(,sc) = 2.5 x 10('10) sec('-1) and (gamma)(,tr) = 5 x 10('9) sec('-1). A lower bound for the coherent trapping or trap scattering radius was determined to be 100 (ANGSTROM);Thermal broadening and temperature dependences of the TPE and SHG signal intensities for both naphthalene and anthracene are presented and are discussed in terms of the polariton fusion model. The experimental data do not agree with the theoretical predictions; this discrepancy is discussed in terms of the anomalous crystal habit (diamond plates) observed in the present investigation;The first report of a longitudinal exciton in a doped organic molecular system also is reported; *USDOE Report IS-T-1259. This work was performed under contract No. W-7405-Eng-82 with the U.S. Department of Energy.