Transient outwardly propagating premixed methane/air flames subjected to joint pressure and equivalence ratio oscillations are investigated using an implicit direct method that couples the compressible flow with realistic chemistry and multicomponent transport properties. Chemistry is a detailed 30 species C-1-C-2 mechanism. The chemical kinetic-transport coupling is compared with results from hydrogen-air flames obtained in earlier work (Malik and Lindstedt, 2010). Increasing flow divergence (positive stretch) decreases the relaxation time tau(CH4)(R) (the time that a flame takes to return to equilibrium conditions after initial disturbance) from 6.0 ms (planar), to 4.5 ms (cylindrical) and 4.0 ms (spherical)-these are about six times longer than tau(H2)(R) from the hydrogen/air flames. However, the nondimensional relaxation numbers n(R) = tau(R)/t(L)(R) (where t(L)(R) is a characteristic flame time scale based upon the thickness of the fuel consumption rate profile) are similar in both types of flames, n(R) approximate to 4.4(P), 3.3(C), and 3.0(S) indicating a similar level of stability to applied disturbances. n(R) deceases by about 40% with increasing positive flow divergence in both flame types under the conditions studied, demonstrating the strong coupling of the heat release to the flame stretch and geometry. Spectral analysis of the pressure fluctuations shows that the spectra scale approximately like E-p similar to omega(-3) in the frequency range 2-10 kHz, and a weak spectral broadening in the spherical case. This is a much weaker kinetic-pressure coupling than in hydrogen/air flames where E-p similar to omega(-2). It was found that increasing flow divergence (from planar to spherical flames) shifts the range of excited frequencies to higher frequencies. It is confirmed that individual chemical species show markedly different responses to the disturbances. Species formed in thin reaction layers are generally not disturbed except with respect to their peak concentration. By contrast, species with broader profiles are generally significantly affected. These findings suggest that combustion processes may be usefully viewed as a spectrum of length scales rather than as just a single global scale. Although the flame adjusts to the local unsteady conditions, some evidence of a time lag or "memory effect" between fuel consumption and the rate of heat relase induced by positive flow divergence is observed.