In many industrial processes both heterogeneous and homogeneous reactions can occur, and these reactions are strongly coupled through heat and mass transfer and reactive intermediates. Surface reactions can heat the boundary layer sufficiently to ignite homogeneous reaction, can deplete the boundary layer of a limiting reactant, and can act as a source or sink of free radicals. We have studied combustion reactions over catalytic foils and in catalytic monoliths for simple oxidations such as CH4 + O2, NH3 + O2, CH4 + NO and NH3 + NO. For most reactions and geometries, we observe heterogeneous and homogeneous ignitions and extinctions and self-sustaining autothermal steady states. The range of compositions for which an autothermal state exists depends sensitively on the inlet gas velocity. For stagnation point flow, reaction over a catalytic foil can be modeled by a one-dimensional boundary value problem in which saddle-node bifurcations correspond to ignitions and extinctions. Computations for a model with simplified kinetics reproduce the experimental dependence on input power to the foil and inlet gas composition. Calculations also show that the dynamics are affected strongly by the inlet gas velocity.