The spectral diffusion dynamics was measured over 3 orders of magnitude in time of a myoglobin-type protein with the heme group substituted by Zn-pheophorbid a. After burning a photochemical hole at 4.2 K, the width of the spectral diffusion kernel is well described by a power law in waiting time with an exponent of 0.24. Spectral diffusion broadening is subject to "aging," viz., to the equilibration time at 4.2 K before hole burning. It decays with a power law in aging time. Deuteration of the solvent has a significant effect on the dynamics of the protein. Spectral diffusion broadening is smaller in the deuterated sample, however, the respective power law is not changed. The aging dynamics, on the other hand, does not seem to be influenced significantly by deuteration. The conclusion is that deuteration influences the fluctuations but not the relaxation. In addition to spectral diffusion, we also measured the recovery dynamics of the hole. It is slowed down tremendously by deuteration, confirming that the photoreaction is based on a light-induced proton transfer.