Ignitions, extinctions, and Hopf bifurcations in methane oxidation were studied as a function of pressure and inlet fuel composition. A continuous stirred-tank reactor was modeled with numerical bifurcation techniques, using the 177 reaction/31 species mechanism. Sensitivity and reaction pathway analyses were performed at turning points to identify the most important reactions and reactive species. Then, simulations were compared with experimental data. Multiple ignitions and extinctions as well as oscillations that are purely kinetically driven were found. Ignition to a partially ignited state with considerable reactivity of methane indicates possible narrow operation windows with high selectivities to partial oxidation products. At 0.1 atm, we found a selectivity of up to 80% to CO at 70% CH4 conversion. The ignition to a fully ignited branch is associated with high selectivity to CO2 and H2O. The C2 chemistry inhibits the ignition of methane to the partially ignited branch. The methane ignition temperature exhibits two branches with respect to pressure, with only the low-pressure branch being dominant. Reaction path analysis at ignition conditions shows that the preferred pathway of CH4 oxidation is to form CO and CO2 through CH2O and CH2(s) intermediates. However, at intermediate to high pressures, the recombination of CH3 to C2H6 also becomes quite significant.