Results obtained using a first-order conditional moment closure (CMC) approach to modeling turbulent nonpremixed flames of hydrogen and hydrogen-helium mixtures are presented. Predictions are based on both k-epsilon and Reynolds stress/scalar flux turbulence closures, and use three kinetic schemes, of varying levels of complexity, that employ 5, 24, and 62 reaction steps. Comparisons with experimental data demonstrate that predictions based on the Reynolds stress turbulence model are superior to those obtained using the simpler eddy viscosity-based approach, although all results are in general insensitive to the kinetic scheme employed. Overall, predictions of major and minor species, and flame temperatures, are in reasonable agreement with data, and compare favorably with the results of earlier investigations that employed both CMC and transported probability density function (PDF) methods. Results do, however, exhibit an underprediction of NO levels in the initial regions of the flames, with an overprediction occurring further downstream. These, and other, shortcomings in the accuracy of the predictions suggest a requirement for further investigation of second-order chemistry and differential diffusion effects, as well as assessments of the applicability of the prescribed PDF and cross-stream average formulation used in the current CMC model. Given the differences observed in predictions obtained using the two turbulence modeling approaches, particularly for NO, such investigations should be conducted within a Reynolds stress turbulence modeling framework. (C) 2003 The Combustion Institute. All rights reserved.