A pure two-fluid model, instead of the Eulerian gas-Lagrangian particle models (particle trajectory models), is used for simulating three-dimensional (3-D) turbulent reactive gas-particle flows and coal combustion. To improve the simulation of the flow field and NOX formation, a modified k-s-k(p) two-phase turbulence model and a second-order-moment (SOM) reactive rate model are proposed. The proposed models are used to simulate NO formation (fuel NO produced by NH3) of methane-air combustion, and the prediction results are compared with those using the pure presumed PDF-finite-reaction-rate model and experimental data. The modified k-epsilon model and SOM model are more reasonable than the standard k-epsilon model and the pure presumed PDF-finite-reaction-rate model. The proposed models are also used to predict the coal combustion and NO formation at the exit of a double air register swirl pulverized-coal burner. The predicted results indicate that a pulverized-coal concentrator installed in the primary-air tube of burner has a strong effect on the coal combustion and NOX formation. (C) 2003 Elsevier Ltd. All rights reserved.