Persistent spectral hole burning is applied to the reaction center, P700, and the light harvesting chlorophyll protein complexes of Photosystem I. A theory for solid state spectral hole burning is developed that is valid for arbitrarily strong linear electron-phonon coupling within the Condon approximation. Persistent photochemical hole burning of the reaction center P700, reveals that a broad (~300 cm[superscript] -1) hole can be burned into the adsorption profile. The hole profile and its maximum position and intensity dependence on burn wavelength are adequately fit by the electron-phonon coupling theory. The results indicate that the absorption and hole profile are dominated by phonon transitions with a Huang-Rhys factor of ~8. A dimer structure for P700 is supported. The similarities to the primary electron donor states of other reaction centers are examined;Nonphotochemical hole burning spectra for the Q[subscript] y transitions associated with the light harvesting antenna complex of Photosystem I are presented. The frequencies and Franck-Condon factors are determined for 51 chlorophyll a and 12 chlorophyll b intramolecular modes. The linear electron-vibration coupling for all modes is very weak with the maximum Franck-Condon factor observed being ~0.04. The linear electron-phonon coupling for protein modes of mean frequency 22 cm[superscript] -1 is weak with Huang-Rhys factor of 0.8. The electron-phonon coupling of the antenna system is compared with that for P700. The intramolecular modes, phonon frequencies, and Franck-Condon factors are used with multiphonon excitation transport theories to analyze the available temperature-dependent data on the kinetics of transport within the core antenna complex. Phonons (not intramolecular modes) mediate excitation transport within the antenna and from antenna to reaction center. The results also indicate that a subunit or cluster model for the antenna provide a more accurate picture than the regular array model for excitation transport.