The effects of solvent viscosity and temperature on the spin-spin relaxation rates 1/T2 of solvent water protons in metmyoglobin and methaemoglobin solutions in the temperature range of 5-50 degrees C have been studied. Solvent viscosity is altered by changing sucrose concentration from 0 to 25% by weight. The magnitude of the protein contribution to the observed relaxation rate 1/T2 decreases with rising solvent viscosity at low temperatures (less than 20 degrees) in contrast to high temperatures. It is shown to be due to the decrease in the rate of exchange of the water molecules from the paramagnetic site (Fe3+ion of heme) within heme cavity with those from the bulk solvent with the rise in solvent viscosity. This effect is interpreted by the dynamic model of protein behaviour in which exchange of the water with Fe3+ion of heme is governed partly by fluctuations of heme cavities between "closed" and "open" states. This approach enables us to estimate the frequency of fluctuations of heme cavities: 7 X 10(4) sec-1 for metmyoglobin and 3 X 10(3) sec-1 for methaemoglobin.