An economic-mathematical model has been developed that describes the mechanism for managing the advanced development of a high-tech organization by implementing managerial effects on its competitiveness. Advanced development is considered as a special model of the organization’s functioning. Its creation is impossible without creating special resources and managerial conditions and widely using many mathematical methods and programming methods, including the method of digital twins of objects and processes, “big data”, etc. The authors discuss the indicators characterizing the basis of the advanced development of a high-tech organization. The problems of innovative development of modern organizations in the rocket and space industry and ways to solve them are examined in detail. Two scenarios for achieving global competitive leadership are presented (progressive market and moderate market). © 2021, Springer Nature Switzerland AG.