The article reviews the main stages of development of single-shaft turbojet engines. Selected construction of these engines are presented divided into three periods (before, during and after World War II) and two main jet engine schemes were discussed (with a centrifugal compressor and an axial compressor). The SO-3 jet engine installed on the TS-11 “Spark” aircraft was chosen to present the method of assessing the safety of structures. The FDM-A diagnostic methods developed in AFIT were used to experimentally verify the technical condition of the engine and FAM-C, based on the analysis of disturbances in the instantaneous rotational speed of the engine shaft. The results of tests related to the assessment of engine shaft misalignment, the assessment of the degree of wear of the engine shaft bearings and the assessment of the shaft clamping force in the bearings are presented. The summary lists the main advantages of single-shaft turbojet engines (simplicity of design for a solution with a centrifugal compressor and high thrust enabling breaking the sound barrier) and their disadvantages (complex design for a solution with an axial compressor and high failure rate of shaft bearing supports as the most loaded engine component).