Even with increasing capabilities of modern computers there is still a need for simplified models of turbulent combustion processes. In order to be useful in practical applications, the models must be capable of predicting such quantities as maximum pressure, maximum pressure rise, and the time of flame arrival at certain positions, quantities which are needed in the design process of safety measures in complex facilities. One possible approach to such problems is the use of a front tracking method. In the present study a front tracking method is used to describe the development of a turbulent flame zone due to convection and propagation/burning in a closed tube. The kinematic description of the flame propagation process makes it possible to eliminate the details of the chemical reactions involved, their effect being summarized in the turbulent burning velocity, which is assumed to be a function of time, turbulence intensity, and laminar burning velocity. The present model is the combination of a front tracking method with a Godunov-type solver for the Euler equations. Results are given for ethylene/oxygen and methane/air mixtures at different equivalence ratios and are compared to experimental data from the literature. While a detonation develops in the ethylene/oxygen mixture, the combustion process in the methane/air mixture proceeds as a comparatively slow deflagration. Both processes can be described with the same model and with reasonable accuracy. (C) 1998 by The Combustion Institute.