In this paper the fluorescence-excitation spectra of individual LH1-RC complexes (Rhodopseudomonas acidophila) at 1.2 K are presented. All spectra show a limited number of broad bands with a characteristic polarization behavior, indicating that the excitations are delocalized over a large number of pigments. A significant variation in the number of bands, their bandwidths, and polarization behavior is observed. Only 30% of the spectra carry a clear signature of delocalized excited states of a circular structure of the pigments. The large spectral variety suggests that besides site heterogeneity also structural heterogeneity determines the optical spectrum of the individual LH1-RC complexes. Further research should reveal if such heterogeneity is a native property of the complex or induced during the experimental procedures.