Abstract - Riley This is a modeling study on turbulent, non-premixed, reacting flows focussing on issues related to the modeling of hydrogen and hydrocarbon diffusion flames burning in air. Issues investigated include the applicability of large-eddy simulations (LES) to turbulent, combusting flows and the influence of differential diffusion of atomic and diatomic hydrogen under turbulent conditions. The validity of large-eddy versions of the flamelet model is studied; comparisons of predictions from LES are made both with laboratory data and with the results of high-resolution, direct numerical simulations. Validity of the modeling of differential diffusion is judged in the context of the Reynolds-averaged (or Favre-averaged) equations and also in the context of the large-eddy simulations.