Electronic excitation energies of a chromophore within a protein environment are not static quantities but fluctuate in time. If an ensemble average is measured, then the relative timescales of measurement and fluctuations determine if an inhomogeneous distribution is observed or if the fluctuations lead to homogeneous broadening. In this chapter, we discuss simple models, which are capable of describing the transition between these two limiting cases. First we derive the transition rate semiclassically for fluctuating transition energy which depends on the Fourier transform of the dephasing function. For Gaussian fluctuations (e.g., for the model of a Brownian oscillator) the second-order cumulant expansion becomes exact. We apply Kubo’s model of exponentially decaying frequency correlations and discuss the limits of long and short correlation time.