The presented work provides a detailed description of the method developed by the authors for coordinating the working process of the main elements of the starting system for a modern gas turbine engine for a civil aviation aircraft: an auxiliary power unit (APU) and an air turbine – starter. This technique was developed in the course of solving the practical problem of selecting the existing APU and air turbine for a newly created engine. The need to develop this method is due to the lack of recommendations on the coordination of the elements of the starting system in the available literature. The method is based on combining the characteristics of the APU and the turbine, reduced to a single coordinate system. The intersection of the characteristic’s lines corresponding to the same conditions indicates the possibility of joint operation of the specified elements. The lack of intersection indicates the impossibility of joint functioning. The calculation also takes into account losses in the air supply lines to the turbine. The use of the developed method makes it possible to assess the possibility of joint operation of the APU and the air turbine in any operating mode. In addition to checking the possibility of functioning, as a result of the calculation, specific parameters of the working process at the operating point are determined, which are then used as initial data in calculating the elements of the starting system, for example, determining the parameters of the turbine, which in turn allow providing initial information for calculating the starting time or the possibility of functioning of the starting system GTE according to strength and other criteria. The algorithm for calculating the start-up time of the gas turbine engine was also developed by the authors and implemented in the form of an original computer program. Keywords: gas turbine engine start-up, GTE starting system, air turbine, methodology, joint work, auxiliary power unit, power, start-up time, characteristics matching, coordination, operational characteristics, computer program.