The present-day methods of supervising the operational use of jet engines are based, among other things, on computerised procedures of monitoring and recording various failure modes, including the surge. This dangerous mode of operation of a turbojet engine occurs quite commonly while operating it. In some cases, it could result even in the engine destruction. What has been presented in this study is the way of applying a non-linear observer of a one-spool single-flow turbojet to generate a computer algorithm to detect the surging. An exemplary application of such an algorithm to monitor the surging that occurs in the K-15 engine has also been shown.