Rate-ratio asymptotic analysis is carried out to elucidate the influence of hydrogen on the structure and critical conditions for extinction of nonpremixed methane flames. Steady, axisymmetric, laminar flow of two counterflowing streams toward a stagnation plane is considered. One stream, called the fuel stream is made up of a mixture of methane (CH4) and nitrogen (N-2). The other stream, called the oxidizer stream, is a mixture of oxygen (O-2), and N-2. Hydrogen (H-2) is added either to the oxidizer stream or to the fuel stream. A reduced mechanism of four global steps is employed in the analysis. Chemical reactions are presumed to take place in a thin reaction zone that is established in the vicinity of the stagnation plane. On either side of this thin reaction zone, the flow field is inert. These inert regions represent the outer structure of the flame. The reactants, CH4, O-2, and H-2 are completely consumed at the reaction zone. The outer structure is constructed employing a previously developed Burke-Schumann (flame-sheet) formulation. It provides matching conditions required for predicting the structure of the reaction zone. In the reaction zone, chemical reactions are presumed to take place in two layers-the inner layer and the oxidation layer. In the inner layer fuel (methane) is consumed and the intermediate species hydrogen and carbon monoxide are formed. These intermediate species and added hydrogen are oxidized in the oxidation layer to water vapor and carbon dioxide. Critical conditions of extinction were predicted from results of the asymptotic analysis and found to agree well with previous measurements. Addition of hydrogen to methane flames promotes combustion by delaying extinction. An important finding of the asymptotic analysis is that the mechanisms by which hydrogen promotes combustion when it is added to the oxidizer stream is different from that when it is added to the fuel stream.