Direct numerical simulations of turbulent nonpremixed hydrocarbon ＇flames＇ are carried out with a constant density approximation. Numerical resolution and stiffness problems which are inherent in oxidation of hydrocarbon Fuels are overcome by using a systematically derived two-step mechanism. The rate constant of the elementary fuel consuming step is carefully relaxed to make the fuel consumption layer amenable to numerical resolution. The Validity of relaxing this rate constant is demonstrated. A detailed discussion of various aspects of the two-step chemistry modeling is given. It is shown that the strategy of using the two-step mechanism with relaxed rate constants does not compromise flame structure and the associated underlying physical processes. Thus, the two-step mechanism is found to be more suitable than a four-step or a one-step mechanism to directly simulate turbulent combustion of hydrocarbon fuels.