An unsteady flamelet model, which will be called the Lagrangian Flamelet Model, has been applied to a steady, turbulent CH4/H-2/N-2-air diffusion flame. The results have been shown to be in reasonable agreement with experimental data for axial velocity, mixture fraction, species mass fractions, and temperature. The application of three different chemical mechanisms leads to the promising conclusion that the state-of-the-art mechanisms yield almost identical results. To explain the still remaining differences from the experimental data, the effects of differential diffusion are discussed. Three possible mechanisms leading to differential diffusion are proposed: Firstly, the occurrence of a laminar mixing layer in a region very close to the nozzle exit; secondly, the molecular diffusivity being of the same order of magnitude as the turbulent eddy diffusivity; thirdly, a typical length scale of the mixing layer thickness bring smaller than the small turbulent eddies leading to a laminar sublayer. By investigating the computational results for the considered configuration, the first mechanism has been concluded to be the only possibility. Further calculations have been performed, which account for differential diffusion by assuming the flow to be laminar very close to the nozzle and switching to unity Lewis numbers downstream of the potential core. The results lead to a significant improvement of the agreement to experimental data. It can be shown from the computational results and the experimental data that the differential diffusion effects arise from this laminar region. However, even though the Lewis numbers are assumed to be unity throughout the remaining part of the flow field these differential diffusion effects remain to a certain extent, even in the far downstream region, affecting for instance the centerline temperature by approximately 100 K. This demonstrates that differential diffusion can cause a strong history effect in turbulent jet diffusion flames.