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The perfectly matched layers [1] technique has been widely and succesfuly used to truncate the computational domain for simulating waves propagation in unbounded domains.We present in this paper a method to construct perfectly matched layers, PML, first for the two-dimensional semilinar wave equation and then for the nonlinear Euler equations.The method presented is an extension of a technique used successfully for the linearized Euler equations [2] [3].We shall focus on the numerical scheme and its stability.We will discuss the construction and the resolution of such numerical models.Finaly we present some numerical results showing the accuracy of the models and the tech niques presented.