The high demands placed on aircraft turbine engines necessitate the use of the latest engine compressors which must be increasingly efficient and more robust due to the increased loads. The key safety issue in this context is to ensure compressor stability over all engine speed ranges and aircraft flight regimes. This paper presents selected areas of research into surge and stall of axial compressors used in aircraft turbine engines based on scientific publications in recent years. On the basis of the analysed literature the authors defined the main research areas into compressor surge, namely: air intake research, compressor research and combined air intake and compressor system research. On the background of the conducted analysis the authors has presented their own areas of research. The aim of this work is to search for an intake-compressor design more passively resistant to stall or surge phenomena without necessity of implementation of complex control systems to prevent compressor stall.