A possible way to introduce hydrogen into the energy matrix would be to enrich traditional fuels like natural gas and propane with hydrogen. Therefore, the study of the flame propagation behavior of these hydrogen enriched fuels becomes important to future industrial applications. In the present work the aim was to experimentally study the effect of hydrogen enrichment of propane and natural gas. However, in order to achieve more generality, the studied mixtures were characterized through the Lewis (Le), Zeldovich (Ze) and the reaction Damköler (Da°) numbers. A total of six mixtures were considered, in which the Ze varied from 4.94 to 8.45, the Le varied from 0.71 to 1.36 and the Da° varied from 14.56 to 36.11. In addition, the obtained results were compared to previous work to assess the effect of the experimental boundary conditions on the flame propagation velocity. The experimental results show that, for mixtures with similar Le numbers, the lower the Ze number the higher the flame propagation velocity. The maximum propagation velocities obtained in the first propagation section of the module are between 18.60 m/s and 57.11 m/s. Therefore, these flames can be considered as weakly accelerating flames. Moreover, the maximum flame propagation velocities showed a good correlation with the product Le × Ze. Regarding the presence of the flame arrester housing without an arrester element, it was observed that it causes an increase in flame propagation velocity. However, when compared to a previous work in which a flame arrester element was inside the housing, the velocity was higher for the present work.