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We compute the e ective wave front speeds of reaction-di usion equations in periodically layered media with coe cents that have small amplitude oscillations around a uniform mean state. We compare them with the corresponding wave front speeds in the uniform state. We analyze a one dimensional model where wave propagation is along the layering direction of the medium and a two dimensional shear ow model where wave propagation is orthogonal to the layering direction. We nd that the e ective wave speed is smaller in the one dimensional model and is larger in the two dimensional model for both bistable cubic and quadratic nonlinearities of the KolmogorovPetrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.

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