The fluorescence of 2-(p-toluidinylnaphthalene)-6-sulfonate associated with beta-lactoglobulin, beta-casein, and bovine and human serum albumins are shown to depend on excitation wavelength. A long-wave shift of the spectra is observed at the long-wave edge excitation, reaching 10 nm and above. A similar phenomenon is found in glucose glass and in glycerol at +1 degrees C, i.e., in systems with delayed dipolar solvent relaxation, but not in liquid solutions. This phenomenon is proposed to be based on relaxation processes in the excited state. There exists a distribution of chromophore microstates with different interactions with surrounding groups which results in heterogeneous broadening of the electronic spectra and allows photoselection of a part of this distribution, being characterized by a low transition energy. The fast structural relaxation results in an altered distribution and, if this is the case, the effect of edge excitation of fluorescence spectra is not observed. If the structural relaxation during the excited state lifetime is absent, this effect is maximal. This interpretation is in agreement with results on the influence of red edge excitation on the low-temperature fluorescence spectra of dyes and with the data on time-resolved nanosecond fluorescence spectroscopy. The results of this work strongly support the significant dye fluorescence spectral shifts on protein binding, being determined not only by polarity changes in their environment, but also by relaxation properties of protein groups in this environment. These results also indicate that on the nanosecond time scale, the structural relaxation around the excited chromophore in proteins may be incomplete.