First- and second-order conditional moment closure (CMC) models are applied to a turbulent CH4/H-2 flame anchored on a bluffbody. Significant extinction is involved as the jet velocity increases for the three test flames: HM1, HM2, and HM3 (in a turbulent nonpremixed flame (TNF) database). The flow and mixing field are calculated with the k-epsilon model with a modified constant, C-epsilon 1. Elliptic CMC formulation is employed to calculate reacting scalar fields with chemical kinetic mechanisms, GRI Mech 2.11 and 3.0. Second-order corrections are limited to three rate-limiting steps to avoid solving a huge number of variance and covariance equations. Even though first-order CMC captures temperature and major species within agreeable limits, the predictions of OH and NO are considerably improved with second-order CMC in both mixture fraction and real space. Results show that the equilibrium assumption performs better than the cold mixture as the conditional inflow boundary condition. There is no noticeable conditional cross-stream dependence downstream, while care needs to be taken in interpretation of the upstream results near the nozzle. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.