An extension of the BML model to the case of Combustion ol lean mixtures with variable equivalence ratio is presented in this paper. The Dilution of both burnt products are fresh reactants by the surrounding air is taken into account by introducing the mixture fraction f in addition to the progress variable c. Statistical analysis of the reactive flow is achieved by using a joint pdf of c and following calculation of mean quantities. Extinction of individual flamelets due to local dilution of fresh recants is also considered. The Influence of dilution, i.e. variable production rate is described. application of this modified model to the case of a stagnating turbulent flame stabilized close to a solid wall shows that the mean flame brush is predicated to be detached from the burner, in agreement with avaliable experimental observartions Qualitative and quantitative modifications of the mean structure of the flame due to dilution are also investigated.