The fluorescence behavior of several dipolar molecules has been studied in three room-temperature ionic liquids, namely, [BMIM][BF4], [EMIM][BF4], and [BMIM][PF6], as a function of the excitation wavelength. Although a large majority of these systems show normal fluorescence behavior with no excitation wavelength dependence, a few systems surprisingly exhibit fairly strong excitation-wavelength-dependent fluorescence behavior in these media. The excitation-wavelength-dependent shift of the fluorescence maximum is measured to be between 10 and 35 nm. The various fluorescence parameters of the systems have been carefully examined to determine the factors that contribute to this kind of behavior, generally not observed in conventional media. It is shown that the existence of a distribution of energetically different molecules in the ground state coupled with a low rate of the excited-state relaxation processes, viz., solvation and energy transfer, are responsible for the excitation-wavelength-dependent fluorescence behavior of some of the systems.