Detailed knowledge about the acceleration of hydrogen-air flames in real geometries is needed to avoid deflagration-to-detonation transition (DDT). Depending on the initial and boundary conditions, the burning velocity of the same hydrogen-air mixture can vary by an order of magnitude. For the modelling of the acceleration process, a 2-D algorithm based on a direct numerical simulation method and including large-eddy simulation is used to calculate the flame folding in the early phase of the process after ignition. Complex mapping functions to realize different obstacle areas in tubes are presented, the effects of combustion on the structure of the turbulence in the flow field and the effects of Bow field instability on the flame development in tubes containing line or expanded obstacles are discussed. Further flame acceleration can lead to DDT. The initiation of detonation by transverse shock waves and its inverse process, detonation quenching, are simulated numerically, using a FCT-algorithm with possible refinement at the detonation front. Reaction kinetics and detonation induction times and lengths are treated rather globally, thus leading to almost tolerable CPU-time. The kinetics are based on an induction parameter model which adapted to a wide range of H-2-air mixtures. The initiation processes of detonation served in the experiments, the development of the detonation cell structure, and quenching based pn geometrical boundary conditions could be reproduced numerically. In particular, the cell structure of the detonation develops automatically from the originally plane front due to small local disturbances in the induction times and lengths. Copyright (C) 1996 International Association for Hydrogen Energy