A new method for the experimental determination of the cross-relaxation (CR) transition rates in liquid solutions of paramagnetic compounds has been developed utilizing a pulsed dynamic nuclear polarization (DNP) technique. In contrast to NMR relaxation, which is proportional to the sum of relaxation rates, the DNP effect is determined by the ratio of transition rates in the nucleus-electron coupled spin system. By use of pulsed DNP, the NMR relaxation rates and DNP data can be obtained in the same experiment. As a result, a set of independent equations for CR and dipole-dipole (DD) transition rates can be derived. The solution of these equations defines individual cross-relaxation and DD transition rates, as well as molecular-kinetic information, and avoids the necessity of performing complicated variable frequency and temperature measurements. A pulsed DNP relaxometer operating at a proton frequency of 0.5 MHz was constructed. The 4-oxo-2,2,6,6-tetramethyl-1-piperidinyloxyl (TEMPONE) stable free radical in benzene was chosen for study as a system with strong intermolecular dipole-dipole interactions, The measurement of individual rates of CR and DD transitions gave us the distance (b = 5.0 Angstrom) between spins I and S for the solvated radical of TEMPONE and also the molecular rotational correlation time (tau(r) = 2.5 x 10(-9) s). Another system studied was the solvated electron in hexamethylphosphorus amide (HMPA) in which scalar and DD interactions an present at the same time. The basic characteristics of this fundamentally important elementary paramagnetic center have been obtained, such as the lifetime of HMPA molecules in the solvent cage (tau(h) = 2.9 x 10(-10) s) and the intermolecular hyperfine constant value (a = 0.08 MHz). Pulsed DNP is shown to be a valuable approach for the study of very weak hyperfine interactions that are not readily detected by other traditional magnetic resonance methods.