A one-dimensional fluid model for a dielectric barrier discharge in CH4/O2 and CH4/CO2 gas mixtures is developed. The model describes the gas-phase chemistry for partial oxidation and for dry reforming of methane. The spatially averaged densities of the various plasma species are presented as a function of time and initial gas mixing ratio. Besides, the conversion of the inlet gases and the selectivities of the reaction products are calculated. Syngas, higher hydrocarbons, and higher oxygenates are typically found to be important reaction products. Furthermore, the main underlying reaction pathways for the formation of syngas, methanol, formaldehyde, and other higher oxygenates are determined.