Constructing a conceptual model as an abstract representation of a portion of the real world involves capturing the (1) static (things/objects and trajectories of flow), (2) the dynamic (event identification), and (3) the behavior (e.g., acceptable chronology of events) of the modeled system. This paper focuses on examining the behavior notion in modeling and current works in the behavior space to illustrate that the problem of behavior and its related concepts in modeling lacks a clear-cut systematic basis. The purpose is to advance the understanding of system behavior to avoid ambiguity-related problems in system specification. It is proposed to base the notion of behavior on a new conceptual model, called the thinging machine, which is a tool for modeling that establishes three levels of representation: (1) a static structural description that is constructed upon the flow of things in five generic operations (activities; i.e., create, process, release, transfer and receive); (2) a dynamic representation that identifies hierarchies of events based on five generic events; and (3) a chronology of events. This is shown through examples that support the thinging machine as a new methodology suitable for all three levels of specification.