Two formulations of a turbulent combustion model based on the approximated diffusion flame presumed conditional moment (ADF-PCM) approach [J.-B. Michel, O. Colin, D. Veynante, Combust. Flame 152 (2008) 80-99] are presented. The aim is to describe autoignition and combustion in nonpremixed and partially premixed turbulent flames, while accounting for complex chemistry effects at a low computational cost. The starting point is the computation of approximate diffusion flames by solving the flamelet equation for the progress variable only, reading all chemical terms such as reaction rates or mass fractions from an FPI-type look-up table built from autoigniting PSR calculations using complex chemistry. These flamelets are then used to generate a turbulent look-up table where mean values are estimated by integration over presumed probability density functions. Two different versions of ADF-PCM are presented, differing by the probability density functions used to describe the evolution of the stoichiometric scalar dissipation rate: a Dirac function centered on the mean value for the basic ADF-PCM formulation, and a lognormal function for the improved formulation referenced ADF-PCM chi. The turbulent look-up table is read in the CFD, code in the same manner as for PCM models. The developed models have been implemented into the compressible RANS CFD code IFP-C3D and applied to the simulation of the Cabra et al. experiment of a lifted methane jet flame [R. Cabra, J. Chen, R. Dibble, A. Karpetis, R. Barlow, Combust. Flame 143 (2005) 491-506]. The ADF-PCM chi model accurately reproduces the experimental lift-off height, while it is under-predicted by the basic ADF-PCM model. The ADF-PCM chi model shows a very satisfactory reproduction of the experimental mean and fluctuating values of major species mass fractions and temperature, while ADF-PCM yields noticeable deviations. Finally, a comparison of the experimental conditional probability densities of the progress variable for a given mixture fraction with model predictions is performed, showing that ADF-PCM chi reproduces the experimentally observed bimodal shape and its dependency on the mixture fraction, whereas ADF-PCM cannot retrieve this shape. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.