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We study the quasi-neutral limit in the steady state Euler-Poisson system for potential flows. Boundary layers occur when the boundary conditions are not in equilibrium. We perform a formal asymptotic expansion of solutions and derive the boundary layer equations. Under the subsonic condition on the boundary and the smallness assumption on the data, the existence, uniqueness and exponential decay of the boundary layer profiles are proved by applying the centre manifold theorem to a dynamical system. We also give a rigorous justification of the asymptotic expansion up to first order in one space dimension.Mathematics Subject Classification: 35B25, 35C20, 35J25, 35Q35

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