Problems of compressor instability have been of concern not only to aircraft engine designers but also for example to operators of industrial power plants. Two types of flow instabilities are known and in this paper only one of them, the surge phenomenon, will be discussed in detail. For the occurrence of these heavy pressure fluctuations the volume of the neighbouring plenum chamber is the important quantity. Here the basic compressor system consisting of a compressor, a duct and a plenum will be analysed in order to show the complete unsteady pressure field. The theoretical model is based on the application of mass, momentum and energy conservation equations of one-dimensional flow. The set of differential equations of hyperbolic type is solved numerically by a ‘predictor'corrector’ scheme. The method itself is an explicit procedure first given by MacCormack /9/. At the interfaces between two components the coupling conditions for pressure and flow velocity are taken from the method of characteristics. The behaviour of the compressor is determined by its performance map, which describes the relationship between pressure and mass flux for all conditions from stable performance to inverse mass flow. For the dynamic change of the pressure development a special compressor characteristic taking into account the unsteady effects is used. This model function is chosen according to a time lagging element often employed in control theory. To demonstrate the capability of the described method variations of different parameters such as mass flow rate, volume behind the compressor, etc. will be presented. The pressure-time history will be compared with experimental data published in the literature. Also the calculated surge frequencies will be discussed. Furthermore it will be examined how a working point of the compressor moves from a stable part of the characteristic to another one, stable or unstable. Finally the general time dependent surge performance is considered in comparison to the quasi-steady characteristic. © 1990, Freund Publishing House Ltd.