Within this paper it is argued that every systematic approach to defining an engineering discipline for computer-based systems in a near axiomatic way must start with laying down adequate theories for all sorts of systems under consideration within the envisioned systematic engineering process. First the nature and contents of a discipline of Engineering of Computer-Based Systems (ECBS) and its activities is elaborated on and then adequate systems theories as conceptual bases for the activities of systems conceptualization and systems design are presented by investigating the activities' nature and the major concepts to form the theories.