For non-stationary objects with parameters, which could be changed significantly during operation, using conventional controllers in the form of proportional-integraldifferential regulators may not provide the required quality of the system. Therefore, it is desirable to create an adaptive automatic control system with the structure and parameters of the control regulator that are purposefully changed to ensure the system adaptation, that is based on information about the properties of the object of regulation and external influences, to the changing operating conditions. The problem of designing adaptive systems is one of the most important in control theory and related fields. This is conditioned by two factors: the complexity of solving the problem as a whole and the presence of a large number of technically diverse situations that need to be adapted and optimized. In the paper, an adaptive system for the automatic control of the speed of a gas turbine engine, which includes a magnetic amplifier, a DC motor with a gearbox, a fuel supply valve and a tachogenerator, is developed. For adaptive control execution, three proportional-integral-differential controllers were proposed: "classic", fuzzy and neurofuzzy. The parameters of the "classic" controller were optimized using linear programming methods. The membership functions and the rule base were proposed for the fuzzy controller. An adaptation algorithm was selected for the neuro-fuzzy controller. Three controllers were used for three engine-operating modes: low-gas, cruiser and maximum during the computer simulation of the system. A comparative analysis of the quality of the three regulators was performed and it is based on the obtained transient characteristics. The derived results can be used in the development of automatic control systems for gas turbine engines.