Computations of combustion in a stratified-charge rotary engine are presented. A three-dimensional model for flows, sprays and combustion which includes the ignition cavity of the engine is used to make these computations. The geometric complexity of the cavity and its coupling with the main chamber is handled by using an unsteady generalized curvilinear coordinate system. The grid is generated using an algebraic grid generator in the main chamber and by solving an elliptic equation in the cavity. Computations of the flows in the cavity are presented for different arrangements of the pilot injector and spark plug and for different timings and fuel injection rates from pilot and main injectors. The dominant feature of the flowfield in the cavity is shown to be the presence of a vortex, induced by the flow in the main chamber, which controls the distribution of the fuel and also the burning rate in the cavity. The computations reveal a strong sensitivity of the combustion process and engine performance to the variables considered in the ignition cavity.