An accurate knowledge of engine exhaust-gas temperatures and velocities is important for engine design and diagnostic efforts. This paper introduces a simple and reliable theoretical model for predicting the instantaneous exhaust-gas temperatures and velocities of a single-cylinder diesel engine. Comparisons of the calculated results with those obtained from experiment have shown good agreement. Based on this agreement, the influence of the engine operating conditions on the exhaust-gas temperatures and velocities can be studied and predicted easily with this model.