The partial oxidation of methane with oxygen in microwave plasma reactors is explored as a process to convert methane to methanol. Controlling the free-radical reactions in the plasma reactors is critical for the selective conversion of methane. To this end, two basic designs of reactors are studied as the key factor in controlling the free-radical reactions. One design has the reactants well mixed upstream of the plasma zone. The other has at least one reactant gas introduced downstream of the plasma zone. The latter type has an inherent advantage that the critical free-radical reactions occur away from the plasma zone so that the intermediates leading to the desired product do not further react in the plasma zone. In addition, if methane is introduced downstream of the plasma zone, the methane dimerization is essentially eliminated.