This paper describes a prediction method applicable to turbulent non-premixed combustion, constrained by the influences of finite rate chemistry. The method is an eulerian particle hybrid based on earlier proposals by Borghi. Such methods are readily adapted to complex numerical grids and offer the potential of computational economy which is acceptable for engineering applications. The present treatment has been extended to encompass extinction. Predictions are herein compared with the data for two, highly-strained, turbulent diffusion flames of the experiments of Masri, Bilger, and Dibble. The principal outcome of this study is that the incorporation of the extinction model enables predictions of good quality to be obtained assuming economical single-step reaction chemistry.