Results are reported from three-dimensional direct numerical simulations of nonpremixed hydrogen-oxygen combustion using a reduced kinetic mechanism in low Mach number, decaying, variable density, isotropic turbulence. The reduced chemical kinetics scheme is based on a seven-species, ten-reaction hydrogen-oxygen mechanism. Realistic kinetic parameters were used. The speed of the entire chemical process was scaled relative to the mixing process by varying an appropriately chosen Damkohler number. The simulation results were compared to predictions of the Conditional Moment Closure model. Next, predictions for the radical species concentrations based on steady-state and partial equilibrium assumptions were compared to simulation results. A model is proposed which gives the thermochemical state as a function of the mixture fraction and a reaction progress variable. The thermochemical states are derived and tabulated from homogeneous premixed calculations. The predictions of this model are compared to simulation data. An expression is derived for the evolution of the error in a manifold approximation.