Object - processes of engine for an TCA design and development in conditions when bankroll, material resources and timing budget are limited; goal - development and practical implementation of the efficient TFE and ATFE for TCA design and development concepts, which are not inferior to the best foreign TFE and ATFE by their scientific and technological level and perfection, in conditions when bankroll, material resources and timing budget are limited; methods - statistical methods that determine the relations, which characterize the development of propulsion engineering and form the efficiency criteria for the design solutions, methods of working process mathematical modeling as for engine as a whole so for its components (in particular, modeling of an afterburner and jet nozzle, experimental research methods for a validation of the mathematical models and revision of results, which were obtained using this models, experimental methods of engine development; results - concepts of efficient engines for trainer-combat airplanes design and development; novelty - a new conception to form parametric shape of highly efficient bypass turbojet engine family for training-combat aircraft in conditions of limited financial, material and time resources was proposed, which is different from the existing ones by the proposed rate of the cost of developing the product and its modification of the criteria for determining the rational combination of base units and engines units projected for the first time, the concept of designing the fuel system for the engine family for training-combat aircraft using a mathematical model, the criteria of minimum power consumption and limiting of fuel heating was proposed for the first time, the concept to design afterburners of training-combat aircraft engines, which allows to optimize the geometry of the diffuser after turbine and the combustion zone by the criteria of minimum take-off weight of the aircraft, to justify the choice of the mixing zone flows of external and internal contours and flame stabilizers, and to match the angular position of starting fuel sprayers and impulsive supply of the starting fuel system "burn track" with the angular position of the turbine stator and flame stabilizer was proposed for the first time, the concept to design jet nozzles for training-combat aircraft, which justifies the choice of convergent ejector nozzle with adjustable external flaps made of light alloys for engines of this type, and using appropriate mathematical model, allows to calculate flow parameters, thrust and thermal condition of flaps was proposed for the first time, the concept of engine fine-tuning on the base of the results obtained during the test of engine prototype, which first extended to engines with afterburners received the further development; the degree of implementation - implemented in design and development ofengines for the trainer-combat airplanes ; industry - propulsion engineering.