The nuclear magnetic resonance relaxation times of solvent water nuclei are known to decrease upon addition of diamagnetic solute protein. For this reason NMR relaxation methods are able to provide information on molecular dynamics changes of water protons and their interaction with macromolecules' surfaces. We present results of measurements of relaxation rates R1 = 1/T1, R2 = 1/T2 and R1ρ = 1/T1ρ in the rotating frame for three proteins: chicken egg white lysozyme, egg white albumin, and bovine serum albumin, obtained at proton resonant frequency of 60 MHz. Besides the relaxation rates dependences on concentration in the 4-23% (g/100 g solution) range, the analysis of the Carr-Purcell-Meiboom-Gill CPMG multi-echo T2 experiments with variable pulse rate τ was performed. The dependences of relaxation rates on protein concentration are linear at low concentration. When protein concentration increases the slope of the straight line rapidly changes at so-called "critical" concentration which depends on MW of the diluted protein. Investigated dispersion of T2, obtained using the CPMG method with a variable pulse rate, for concentrations higher and lower than the "critical" one, exhibits unequal behavior. At high concentration one-exponential curves and at low concentration two-exponential curves correspond closely with experimental data. The obtained parameters of exponents allow an estimation of the ratio of the amount of water with the determined motion freedom, that is free and bounded water, in solution. We showed that the CPMG dispersion method applied to aqueous protein solutions may widen the current understanding of the nature of molecular dynamics of hydrated water protons in non-perturbed environment.