The influence of solvent viscosity on the surface and internal structural dynamics of the protein myoglobin is studied using ultrafast infrared vibrational echo measurements of the pure dephasing of the A(1) CO stretching mode of myoglobin-CO (Mb-CO). The dephasing reflects protein structural fluctuations as sensed by the CO ligand bound at the protein's active site. Measurements made as a function of solvent viscosity at 295 K show that the pure dephasing has a marked dependence on viscosity. In addition, the pure dephasing of Mb-CO in the solvents trehalose and 50:50 ethylene glycol:water are compared as a function of temperature T(10-295 K). The pure dephasing data in the two solvents have identical T-1,T-3 temperature dependences at low temperatures, where both solvents are glassy solids. At higher temperatures. the Mb-CO pure dephasing has a much steeper temperature dependence in ethylene glycol:water, which is a liquid, than in trehalose, which is a glass at all temperatures studied. The steep temperature dependence in liquid ethylene glycol: water is described as a combination of a viscosity-dependent component and a temperature-dependent component. The viscosity-dependent data are analyzed using a theory that connects the fluctuations of the protein surface to the solvent's viscoelastic response. When the solvent's viscosity is lowered, the increased rate of fluctuation of the protein's surface allows more rapid internal protein dynamics, which result in more rapid dephasing. Good agreement is obtained fur physically reasonable parameters. The experimental echo decay times are proportional to the cube root of the solvent viscosity eta (1/3) This proportionality is characteristic of protein structural fluctuations that give rise to CO frequency fluctuations that are in the spectral diffusion regime (relatively slow evolution).