An opposed flow non-premixed flame (OFNPF) in a narrow channel was chosen as a model of a non-premixed flame in a mesoscale combustion space or micro-combustor. The stabilization limits and behaviors of methane-air flames and propane-air flames were compared for various experimental parameters such as flow velocity, nozzle distance, nozzle width, channel gap, and fuel dilution. Flames could be stabilized in a wide range of strain rates (0.9-150 s(-1)) and dilution ratios (similar to 80% nitrogen at the fuel side). The flame extinction limits were classified into three types and their mechanisms were investigated: higher-strain-rate (HSR) extinction limit determined by the flame stretch, lower-strain-rate (LSR) extinction limit determined by the conductive or convective heat loss from the flame, and fuel-dilution-ratio (FDR) extinction limit determined by the decrease in the heat release rate from the flames. The HSR extinction limits in mesoscale channels could be explained with a modified strain rate, and the LSR extinction limits could be explained by employing a premixed quenching theory in which the heat loss through the dead space near the wall was considered as a major extinction mechanism. Finally, the variation of the extinction limits with the FDR in both the HSR and the LSR conditions could be explained with a modified global reaction rate in which the variations in flame temperature and species concentrations were reflected. This study provides an essential model for the stabilization and extinction of non-premixed flames in mesoscale combustion spaces.