Ensuring reliable and timely diagnostics and control of a rotating stall and self-oscillations on the fan blades and the first stages of GTE compressors for aviation and ground application with special bench tests, at the engine development stage, is a relevant topic. To solve the problem, spectral analysis of the vibration sensor signals, the bench control system, registered during the engine check for unstable modes of operation, was performed. Diagnostic components that appear in the signals of vibration sensors with rotating breakdown and auto-oscillations at the moments of the appearance of stresses on the blade components of the strain gauge signals are revealed. The existence of the dependence of the blade component and the diagnostic components on the rotor speed is determined. The dependence obtained makes it possible to isolate diagnostic components from the broadband signal, similar to the construction of vibrations using the first rotor harmonics. A method was developed to control rotating breakdown and self-oscillations in the course of GTE tests, with designated limit levels proportional to the stress levels on the fan blades. It is shown that the best, from the ease of implementation and efficiency, a method of monitoring unstable modes of operation is the method with the use of servo filters at diagnostic frequencies. At the same time, it is technically easier to use the available vibration sensors used in monitoring the first rotor harmonics than to install additional pulsation sensors, performing modifications to the engine design, without mentioning the work package required for strain gauging. Besides, the set of signals of standard and technological vibration sensors of the bench control allows determining the diagnostic frequencies of any element of the engine design: fan, compressor, turbine. After tuning the vibration equipment to the required diagnostic frequencies, a specialist with no skills in diagnosing vibration signals can maintain control, which is convenient for the first tests of the engine in operation, where the experimenter controls the flight.