An experiment was set up to investigate the correlation between flame velocity and flame stretch in moderately stretched laminar jet flames of methane-air mixtures at different equivalence ratios. Gas flow velocities were obtained by Particle Image Velocimetry (PIV) from images of axial sections of seeded flows, and the location of the flame front was related to the gradient of luminosity. Flame stretch was determined and shown to be mainly due to flame curvature, with a small contribution from the gas strain rate. Inlet gas velocities not much larger than the planar flame velocity led to short rounded flames for which the classical Markstein relation was experimentally validated at any point of the flame fronts. However, the Markstein relation ceases to be uniformly valid for larger inlet gas velocities, in the order of ten times the planar flame velocity, for which the flame adopts a slender shape. These tall flames are nearly conical and obey the Markstein relation far from their tips, but a superlinear increase of flame velocity with stretch is observed when the tip is approached. Furthermore, the local velocity of these flames depends not only on the stretch but also on the inlet velocity of the gas. This behavior has been analyzed in terms of an empirical correction to the Markstein relation that is quadratic in the flame stretch with a coefficient that depends on the gas inlet velocity. The experimental results suggest that this coefficient is zero below a certain threshold value of this velocity and increases as the square root of the excess of gas inlet velocity above this threshold. This kind of sharp transition controlled by the velocity of the incoming gas is reminiscent of a typical critical behavior and is tentatively taken to reveal a stability exchange between rounded (weakly curved) and slender (strongly curved) flames. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.