In this report some experiences that were made with high-order finite-volume ENO-schemes are reported. In a first section the most important parts of the numerical method, the reconstruction and the choice of the stencil are presented, at the example of the linear advection equation. The extension of the ENO-algorithm to the Euler and the Navier-Stokes equations is shown. The stability-properties and the precision of ENO-schemes are discussed. In a second section the presented method is applied to the full Navier-Stokes equations. The chosen test-case concerns a compressible mixing-layer at transonic and subsonic Mach-numbers. Computations with third-order ENO show that the numerical method captures shocks and contact discontinuities well. Fourth-order ENO-computations make difficulties on fine grids.