A two-step reaction model is used to analyze the interaction between (1) a fuel-air multi-stratified vortical mixing layer and (2) strong pressure waves caused by rapid combustion of the mixed region. During the Ist stage induction period where no heat release occurs, a large-scale vortical structure evolves, generating a wide contact surface and extended mixing between fuel and air. During the ensuing 2nd stage exothermic reaction, the locally premixed fuel-air rapidly burns and produces strong pressure waves. The results show that: (1) the 2nd stage exothermic reaction starts at the core of each vortex where ＇＇reactivity index = (Y-CH4)(Y-o2)(2) exp(-Ze/T*)＇＇ is high; (2) then the generated strong pressure waves promote the reaction at the outermost stratified region of each vortex; (3) spot-like flames formed in the premixed region propagate toward the surrounding unburned region, due to conventional defraglation mechanism; (4) on the other hand, delayed combustion starts in the braid region where mixing is highly inactive; (5) finally, after the consumption of premixed reactants, a diffusion flame with a low mass consumption rate prevails.