Evolution equations for the coupled relaxation of densities and temperatures for the components in nonideal partially ionized plasmas are given. In these equations many-body effects, such as screening, self-energy, and lowering of the binding energy, are included. The coupled equations are solved numerically for a hydrogen plasma consisting of electrons, protons, and atoms. Impact ionization, three-body recombination, and elastic processes are taken into account. Thermal relaxation times are determined and the results are compared with those from the literature. The influence of many-body effects on the evolution process are discussed. In some cases, a significantly increased lifetime of the two-temperature regime is found. (C) 1996 American Institute of Physics.