Systems are everywhere around us, such as products, production lines, the Internet, companies, schools, hospitals, airports, communities, cities, countries, governments, and military forces. System researchers and engineers always strive to achieve their desired system behaviors. Thus, this paper aims to solve two fundamental problems of systems engineering: what determines the behavior of a system and how to design a satisfactory system for the expected behavior. First, we determine the dimensions of a relationship flow, such as information flow, material flow, and capital flow. Second, we develop new theorems and propositions to solve the first problem. For example, they show that, for a given behavior of a system, if the dominant subsystem of the behavior has the basic level for the behavior, the behavior is only determined by its input flow and relationship flows at or above the basic level, all of which are collectively referred to as total relationship flow (TRF). Third, we develop a relationship flow diagram which is of great significance to system design, just as a circuit diagram to circuit design, and a TRF-oriented system design framework to solve the second problem. In order to show how the framework works, we apply it step by step to the schematic design of an airport system for the required passenger departure procedure service behavior, and get a system example; using this framework to design a system will greatly simplify the complexity of development and improve the maintainability of the system. Therefore, our findings provide a new theory for systems engineering and improve its methods and tools systematically.