In some turbulent flows involving premixed turbulent combustion either heat transfer or nonuniformity of the mixture leads to variations of the enthalpy. Here we extend the Bray-Moss model for the thermochemistry of such combustion to include nonisenthalpic flows. Applications are identified to boundary layers with reactants injected through a porous surface involving heat transfer, to channel flows with product streams serving as flameholders and to open flames discharging into quiescent air