The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organises seminars on subjects concerning the algorithmic treatment of par­ tial differential equations. The topics are discretisation methods like the finite element and the boundary element method for various types of applications in structural and fluid mechanics. Particular attention is devoted to the advanced solution methods. The series of such seminars was continued in 1994, January 14-16, with the 10th Kiel-Seminar on the special topic Fast Solvers for Flow Problems at the Christian-Albrechts-University of Kiel. The seminar was attended by 100 scientist from 9 countries. 23 lectures were given, including two invited survey lectures. The central topic of most of the contributions are the Navier-Stokes equations. The authors discuss robust methods, parallel implementations, defect correction techniques, adaptive methods including error estimators, domain decompositions and FEM-BEM coupling. The invited lectures concern the hierarchical multigrid method for unstruc­ tured grids and structured adaptive finite-volume multigrid for compressible flows.