Three-pulse echo peak shift measurements were performed on the B875 and B850 bands of detergent-isolated LH1 and LH2 complexes at room temperature. The peak shifts are much larger and decay much faster than typically observed for dye molecules in solution. Simulations of the peak shifts based on the optical transition frequency correlation function, M(t), are presented. M(t) includes contributions from rapid protein fluctuations, vibrational motion, and energy transfer. The model reproduces the room temperature absorption spectra of B850 and B875, shows that the coupling of electronic and nuclear degrees of freedom is much weaker than for dyes in solution, and identifies contributions to the line shapes that may be important to the energy transfer processes. The implications of these results for the extent of electronic delocalization in LH1 and LH2 are also discussed. Although the role of coherence transfer still needs to be understood, the results are shown to be consistent with the use of weak-coupling excitation transfer models of B850 and B875.