This experimental investigation considers steady two-dimensional rich and lean premixed methane-air flames established in two configurations, one a two-dimensional slot burner and the other an axisymmetric coannular burner. The flames contain a curved premixed reaction zone that has a tip. Flame curvature is a parameter that significantly influences the structure and propagation of premixed flames through its contribution to flame stretch. In a previous investigation we focused primarily on stretch effects along the planar portion of the premixed reaction zones of various slot-burner methane-air rich (partially) premixed flames. In this study we concentrate on stretch effects along the curved portion of the reaction zones of those flames, employing the same methodology, and also extend our analysis to lean flames. Instantaneous temperature measurements were made by using holographic interferometry. Velocity vectors were determined by using particle image velocimetry, and the flame reaction-zone topography was characterized by imaging C-2(*)-chemiluminescence. It is possible to identify a constant approximate to 1100 K temperature contour along the inner premixed reaction zone by comparing the C-2(*)-chemiluminescence image and the holograms, The flame speed at the flame tip is enhanced above the corresponding unstretched value. We show that the Markstein relation S-u/S(u)degrees = 1 - L kappa /S(u)degrees must be suitably modified along the curved portion of the reaction zones. The response to stretch differs in the planar and curved regions of the premixed reaction zone. However, this classical relation is well suited along the planar portions of the reaction zones. Although the propagation speed varies along the planar region of the reaction zone, the corresponding differences are larger along the curved region, We consider a variation of the Markstein expression S-u = CS(u)degrees - L kappa. The value of C in the literature is generally considered to equal unity. We have developed an empirical relation for the curved region and have empirically determined from our data that the best fit for the constant C is related to the unstretched flame speed and the value of the reaction-zone speed at the inner premixed flame tip, i.e., C approximate to S-u,S-up/10S(u)degrees. The value of the constant C does not have a universal value due to geometry effects. A limitation of this expression is that it does not provide the expected solution S-u = S(u)degrees at zero stretch. This discrepancy is most likely due to a poor resolution of the velocity data in the region where the flame transitions from a planar to a curved topography. The response of the flame speed at the larger stretch values differs from that at weaker stretch. The value of Ka can be increased by increasing the stretch rate kappa or the mixture diffusivity D-M,D-u, or by decreasing the laminar flame speed.