A model to simulate numerically self-ignition and combustion of initially non-premixed turbulent systems is proposed. Its development is based on Direct Numerical Simulations (DNS) of turbulent mixing layers between cold fuel and a hot oxidizer. The direct numerical simulations are used to better understand the physical mechanisms controlling mixing, self-ignition, and establishment of combustion inside turbulent mixing layers. They are also used to define the mathematical formulation of the model, and to test its assumptions. The model has a component for self-ignition and an additional component for subsequent high-temperature combustion. Self-ignition is simulated using an approach based on presumed Probability Density Functions (PDFA model) that takes into account the effects of turbulence on mixing formation during and after self-ignition. The PDFA model describes the turbulent reacting flow using a mixture fraction variable and a generalized reaction progress variable, The high-temperature combustion, established after self-ignition has occurred, is computed using a flamelet approach (CHI model). The two model components are coupled by a function of the progress variable deduced from DNS results. The PDFA-CHI model is implemented in a Reynolds averaged Computational Fluid Dynamics (CFD) code, and is tested in one-dimensional (1D) and two-dimensional (2D) configurations. The computational results reproduce ignition phenomena in the turbulent held similar to the DNS calculations. (C) 2001 by The Combustion Institute.