This volume contains the proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics, held at the Ecole Polytechnique Federale de Lausanne, Switzerland, on September 25-27, 1991. This conference, as weil as the preceding eight ones, was organized by the GAMM Committee on Numerical Methods in Fluid Dynamics. 1t was probably also the last one in this successful series of conferences, since in the future, a bi-annual European meeting on Computational Fluid Dynamics will be organized by ECCOMAS, a new organization, representing all existing European professional societies working in this field. The conference was attended by about 100 registered participants coming from all corners of the world. These proceedings contain the written version of the 56 papers presented during the meeting. In order to eliminate all kinds of errors, omissions, spelling mistakes, etc. these papers have been reviewed by an ad hoc scientific committee. As a result of this work a good deal of the papers were sent back to the authors for correction. This procedure has somewhat delayed the publication of this volume. We feel, however, that this has been a worth while effort. The subjects treated during the meeting represent weil current interests in CFD. For instance, multigrid and multiblock techniques for viscous as weil as inviscid 3D flows were presented. Similarly, finite rate chemistry hypersonic flows still attracts many scientists due to the continuation of the Hermes Project.