The paper describes the method of selecting the working process parameters of a family of small-scale gas turbine engines (GTE) with common core. As an example, the thermodynamic design of a family of small-scale gas turbine engines (SGTE) with common core was carried out. The engine family includes a small-scale turbojet engine (STJE) and a gas turbine plant (GTP), which electric generator is driven by power turbine. The selection of rational values for the working process parameters of STJE and GTP was carried out in CAE system ASTRA on the basis of nonlinear optimization of these parameters, taking into account functional and parametric constraints. The quantitative results of deterioration in the performance of the engines of the family with common core are obtained in comparison with the engines with the optimum core for each type. However, the advanced creation of a common core can reduce the cost and timing of the engine creation, ensure its higher reliability (due to the development of the base common core) and reduce the cost of its production. The method of selecting the parameters of the working process of the GTE family with common core presents the solution to more complex problems, such as the possibility of developing a family consisting of five engines: a turbojet engine, turbofan engine, turbofan engine with a complex cycle, GTE with power turbine (GTE-PT), GTE-PT with recovery.