It has been shown that pressure waves can have a large effect on the burning rate of flames. For sharp changes in pressure, recent studies by Batley, McIntosh and Brindley [2] have indicated that the mass flux is dependent on the origin chosen as the frame of reference. Consequently, the structure of the flame is altered by the passage of a pressure disturbance as gas flows at different rates through different locations of the flame. In this paper, pressure disturbances on the relatively slow diffusion time scale are studied. This is when tau approximate to 1 where tau is defined as the ratio of a typical diffusion time to a typical acoustic time. This formulation leads to equations for the flame evolution which are valid for pressure in the range 0 less than or equal to p less than or equal to 1 + O(1/theta). Numerical investigations are carried out on these nonlinear equations. Results indicate that for sufficiently large pressure drops, the structure of the flame alters significantly even for disturbances on the slower time scale. For pressure pulses, the flame thickness can increase to over twenty times its original value and the local mass flux can go negative. Thus, the solutions obtained from considering the equations with jump conditions across the flame are no longer valid because the width of the reaction zone cannot be neglected. Therefore, it is demonstrated that whilst qualitative long term behaviour can be predicted using the equations with jump conditions, transient behaviour and quantitative results can only be obtained by numerically solving the fully nonlinear problem.