The response of premixed hydrogen/air flames propagating outwardly through moderately inhomogeneous fuel distributions and subjected to stretch and simultaneous pressure and equivalence ratio oscillations was explored computationally using an implicit method (N.A. Malik, 2009a, 2009b). The method is second-order accurate in space and time and solves the fully compressible Eulerian balance equations coupled to the detailed chemistry and transport properties. The impact of increasing curvature was investigated through the use of planar, cylindrical, and spherical geometries. 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. For pressure oscillation frequencies in the range of 200-1000Hz and amplitudes of 1-2% of atmospheric pressure, a spectral response is observed centred around 5kHz and scaling approximately as -2 under the persent conditions, thus indicating a coupling between the oscillations and reaction layers. The results appear to be correlated with the disruption of the thermochemical structure of the flames. Although the flames adjust to the local conditions, some evidence of a time lag or memory effect between fuel consumption and the rate of heat release is observed. The influence of stretch (curvature) is seen in the reduction in the flame relaxation times R from 1.1ms in a planar flame to 0.65ms in a spherical flame; R is the time taken for the system to return to the prevalent mean conditions after a disturbance. Under unsteady random pressure fluctuations, the Markstein number shows large variations, indicating a breakdown of the Markstein hypothesis.