A theory is developed that is suitable for describing a two-species thermalization process in a plasma with parameters suitable for recombination to take place. Recombining plasmas have recently been produced using positrons and antiprotons [M. Amoretti et al., Nature (London) 419, 456 (2002); G. Gabrielse et al., Phys. Rev. Lett. 89, 213401 (2002)]. The theory is not restricted to large Coulomb logarithm values, and correspondence with prior theory is shown in the limit of large Coulomb logarithm values. The theory applies for two plasma species, each having a Maxwellian velocity distribution and being weakly correlated.