Laser photolysis of H2S at 248 nm and at 193 nm was used to generate nonequilibrium distributions of translationally energetic hydrogen atoms at high dilution in a flowing moderator gas (N-2 or Ar). The pulsed laser photolysis/laser-induced fluorescence ''pump-and-probe'' method allowed the measurement of the line shapes of the moderated H atom Doppler profiles as well as the concentrations of D atoms produced in the reactive collisions between the H atoms and Dr or D2O reagents. H and D atoms were detected with sub-Doppler resolution via (2p(2)P <-- 1s(2)S) laser-induced fluorescence. The measured H atom Doppler profiles were used to describe the evolution of the initially generated nascent nonequilibrium H atom speed distribution toward its equilibrium Maxwell-Blotzmann form. In this way the excitation function and reaction threshold for the reactions H + D-2 --> HD + D and H + D2O --> HOD + D could be determined for the first time from the measured nonequilibrium D atom formation rates and single-collision absolute reaction cross sections measured at higher collision energies.