The concept of Markstein numbers with respect to unburned and burned gases is first reviewed. We next present numerical simulations of methane-air and propane-air flames in the counterflow configuration using a detailed chemical kinetic model consisting of 469 reactions and 71 species. Markstein numbers of these flames, as a function of equivalence ratio, are computed with respect to both the unburned and burned gases. It is shown that the values of Markstein number relative to the unburned and burned gases are not equal and may even have opposite signs, as supported by asymptotic theory. The values from these numerical simulations are then compared to the values published in the literature for the same mixtures. We show that experimental values in the literature, obtained from the expansion rates of spherical flames, are very close to our numerical values of the Markstein numbers with respect to the burned gases, simply re-normalized by the gas density ratio. These results support the idea that flames respond similarly for equal values of a small characteristic stretch. We also find close agreement with an experimental measurement made in the unburned gases on a counterflow propane flame. However, some of our values evaluated in the unburned gases are significantly different from those in the literature, obtained indirectly using measurements of the growth rate of unstable structures on planar flames. We present evidence to suggest that the results of asymptotic flame theory, used to obtain the indirect measurements of Markstein numbers, are not quantitatively applicable when the effective Lewis number of the mixture is not close to unity.