The propagation rates of advancing and retreating non-premixed edge flames in a slot-jet counterflow were measured as a function of strain rate for varying jet spacing, mixture strength, stoichiometric mixture fractions $(Z_{st})$ and Lewis numbers (Le). Methane and propane fuels were tested and nitrogen and carbon dioxide were used as inerts. As results, we could identify igniting fronts, retreating fronts, two total extinction limits, and short-length edge flames. A burner separation affected to a low extinction limit only. Regimes for advancing and retreating edges together with total extinction were mapped in terms of normalized flame thickness and heat loss factor for $CH_4/O_2/N_2$ mixtures. Edge flames for $Z_{st}$ > 0.5 behaved like a stronger mixture while for $Z_{st}$ < 0.5 showed deteriorated feature, because of relative locations of a non-premixed flame and intermediate species such as CO and $H_2$. Furthermore, due to the relative importance of heat loss, propagating speeds of edge flames were significantly enhanced in $CH_4/O_2/CO_2$ mixtures (Le < 1) demonstrating increasing stability limits. However $C_3H_8/O_2/N_2$ mixtures (Le > 1) showed opposite result.