Earlier studies of the magnetic field dependence of the nuclear spin magnetic relaxation rate of solvent protons in solutions of diamagnetic proteins have indicated that this dependence (called relaxation dispersion) is related to the rotational Brownian motion of solute proteins. In essence, the dispersion is such that 1/T1 (the proton spin-lattice relaxation rate) decreases monotonically as the magnetic field is increased from a very low value (approximately 10 Oe); the dispersion has a point of inflection at a value of magnetic field which depends on protein size, shape, concentration, temperature, and solvent composition. The value of the proton Larmor precession frequency nu(c) at the inflection field appears to relate to tau (R), the rotational relaxation time of the protein molecules. We have measured proton relaxation dispersions for solutions of various proteins that span a three-decade range of molecular weights, and for one sample of transfer ribonucleic acid. We have also measured deuteron relaxation dispersions for solutions of three proteins: lysozyme, carbonmonoxyhemoglobin, and Helix pomatia hemocyanin with molecular weight 900 000. A quantitative relationship between both proton and deuteron dispersion data and protein rotational relaxation is confirmed, and the point is made that magnetic dispersion measurements are of very general applicability for measuring the rotational relaxation rate of macromolecules in solution. It has been previously shown that the influence of proton motion on the relaxation behavior of the solvent is not due to exchange of solvent molecules between the bulk solvent and a hydration region of the protein. In the present paper, we suggest that the interaction results from a long range hydrodynamic effect fundamental to the situation of large Brownian particles in an essentially continuum fluid. The general features of the proposed mechanism are indicated, but no theoretical computations are presented.