This chapter discusses the direction of development of promising multimode aviation gas turbine engines (GTE). It is shown that the development of GTE is on the way to increase the parameters engine workflow: gas temperatures in front of the turbine (T*G) and the degree of pressure increase in the compressor (P*C). It is predicted that the next generation engines will operate with high parameters of the working process, T*G = 2000–2200 K, π*C = 60–80. At this temperature of gases in front of the turbine, the working mixture in the combustion chamber (CC) is stoichiometric, which sharply narrows the range of stable operation of the CC and its efficiency drops sharply in off-design gas turbine engine operation modes. To expand the range of effective and stable work, it is proposed to use an advanced aviation GTE: Adaptive Type Combustion Chamber (ATCC). A scheme of the ATCC and the principles of its regulation in the system of a multi-mode gas turbine engine are presented. The concept of an adaptive approach is given in this article. There are two main directions for improving the characteristics of a promising aviation gas turbine engine. One is a complication of the concepts of aircraft engines and the other one is an increase in the parameters of the working process, the temperature of the gases in front of the turbine (T*G) and the degree of increasing pressure behind the compressor (π*C). It is shown how the principles of adaptation are used in these areas. The application of the adaptation principle in resolving the contradiction of the possibility of obtaining optimal characteristics of a high-temperature combustion chamber (CC) of a gas turbine engine under design (optimal) operating conditions and the impossibility of their implementation when these conditions change in the range of acceptable (non-design) gas turbine operation modes is considered in detail. The use of an adaptive approach in the development of promising gas turbine engines will significantly improve their characteristics and take into account unknown challenges.