Both a two-dimensional thermokinetic model and a detailed multidimensional one, only tractable by numerical computation, are applied to the high-pressure, low-temperature, noncatalytic, direct partial oxidation of methane in a continuous stirred tank reactor (CSTR). It is shown that all the phenomena encountered experimentally in this system so far can be accounted for qualitatively by the two-dimensional model and semiquantitatively by the numerical approach. These phenomena include the parametric dependencies of methanol selectivity and yield and the occurrence and significance of hysteresis, bifurcation, oscillation, and extinction, of the direct partial oxidation reaction.