The diffusive-thermal pulsating instability of Le > 1 flames can considerably alter global quantities such as the flammability limit and mass burning rate, making its study practically relevant. In the present study we investigate the behavior of pulsating flames in unsteady flow fields using one-dimensional and two-dimensional flame simulations of laminar premixed rich hydrogen/air flame in a counterflow configuration, focusing on the response of the flame to imposed fluctuations in strain rate and equivalence ratio. These effects become important when the flame propagates in an unsteady flow field, for example, in turbulent flows. In the case of strain rate forcing, the flame is found to undergo oscillatory extinction if the forcing frequency is less than the pulsation frequency. For strain rate forcing frequencies higher than the pulsation frequency, the flame is found to be largely unresponsive to the upstream flow velocity fluctuations. The parametric study for equivalence ratio forcing shows that the pulsating instability is promoted with increasing inlet velocity, increasing amplitude and mean value of the imposed composition fluctuation. At the same time, it is observed that increasing the frequency of the imposed oscillations may attenuate the pulsating instability. Moreover, it is found that a flame subjected to pulsating extinction may be able to sustain pulsating combustion if forced with high-frequency inlet composition variation. Based on the insights gained from one-dimensional simulations, two-dimensional simulations of these pulsating flames are performed to provide additional insights on the shape and location of cells and cusp formation in these flames. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.