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The interaction of a purely mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible couple-stress fluid between infinite parallel walls on which a sinusoidal travelling wave is imposed. A perturbation solution to the complete set of Navier-Siokes equations in found for the case in which the frequency of the travelling wave and that of the imposed pressure gradient are equal. The ratio of the travelling wave amplitude to channel width is assumed to be small. For this case a first order steady flow is found to exisi, as contrasted to a second order effect in the absence of the imposed periodic pressure gradient. The effects of the various parameters entering into the problem are discussed numerically.