A mathematical model of ignition and detonation of bituminous coal-dust suspensions is developed in the frame of two-velocity two-temperature approach of the heterogeneous media mechanics. The reactions of pyrolysis, volatile combustions, and coke combustion and the temperature non-homogeneity of the particle are taken into account. The model is verified by the experimental data on the ignition delay times in transient shock waves. An analysis of the ignition study reveals a considerable effect of the velocity nonequilibrium and the stagnation temperature on the dynamics of devolatilization and ignition delays. The numerical examples of the shock wave and detonation structures in a coal dust in oxygen are presented. (C) 2008 Elsevier Ltd. All rights reserved.