We construct Lp-estimates for the inhomogeneous stationary Oseen system studied in a two dimensional exterior domain with inhomogeneous slip boundary conditions. The main part of the talk is a presentation of results for the half space , which are substantial for the exterior problem. Main tools are given by the Fourier analysis, to obtain maximal regularity estimates. In addition, these optimal estimates show us a difference in points in front of the obstacle and behind the obstacle. The former are typical for elliptic problems while the latter show disturbance, which is typical for parabolic problems.