In this study, we aimed to evaluate the extinction limits of fuel-rich and fuel-lean flames created in a nonpremixed coaxial swirl burner of combustion substrates. The experiments were performed with three types of fuels: methane and two mixtures of CH4/CxHy/N-2. The analyzed fuels reflected varied composition of the natural gas containing methane, ethane, propane, butane, and nitrogen. The examination of the extinction limits of flames isolated from the surroundings with a quartz tube was based on the limit ratios of equivalence (Phi). Results showed that an increase in the stream of methane directed toward the burner improves blowout limits as determined by the equivalence ratios. However, this pattern was not observed for the other studied fuels. A concurrent increase in the content of CxHy and N-2 in natural gas implies worsening of extinction limits of fuel-lean flames and improvement of extinction limits for fuel-rich flames. Thermodynamic calculations using the FactSage 6.3 software package were also performed, specifying the adiabatic temperature of flames and the equilibrium composition of exhaust gases in the areas close to the extinction of flames. It was found that it is possible to estimate the improvement or deterioration of the blowout limits of flames resulting from changes in the composition of natural gas based on the equilibrium exhaust composition.