The response to strain of stochiometric methane-air flames stretched in counterflow geometries is investigated theoretically using asymptotic methods. The special case of weak strain is considered. The asymptotic analysis is based on a systematically reduced three-step kinetic mechanism for methane oxidation. An expression for the Markstein number is derived and compared with results obtained previously from activation-energy asymptotics on the basis of a global one-step reaction. Comparisons to numerical results and experimental data available in the literature are performed.