Under high-excitation irradiance conditions in one- and two-photon induced fluorescence microscopy, the photostability of fluorescent dyes is of crucial importance for the detection sensitivity of single molecules and for the contrast in fluorescence imaging. Herein, we report on the dependence of photobleaching on the excitation conditions, using the dye Rhodamine 6G as a typical example. The different excitation modes investigated include 1) one-photon excitation into the first-excited singlet state in the range of 500 to 528 nm by continuous wave and picosecond-pulsed lasers and 2) two- and one-photon excitation to higher-excited singlet states at 800 and 350 nm, respectively, by femtosecond pulses. Experimental strategies are presented, which allow resolving the photophysics. From single-molecule trajectories and fluorescence correlation spectroscopy, as well as with a simple theoretical model based on steady-state solutions of molecular rate equation analysis, we determined the underlying photobleaching mechanisms and quantified the photokinetic parameters describing the dependence of the fluorescence signal on the excitation irradiance. The comparison with experimental data and an exact theoretical model show that only minor deviations between the different theoretical approaches can be observed for high-pulsed excitation irradiances. It is shown that fluorescence excitation is in all cases limited by photolysis from higher-excited electronic states. In contrast to picosecond-pulsed excitation, this is extremely severe for both one- and two-photon excitation with femtosecond pulses. Furthermore, the photostability of the higher-excited electronic states is strongly influenced by environmental conditions, such as polarity and temperature.