Behavior modeling and software architecture specification are attracting more attention in software engineering. Describing both of them in integrated models yields numerous advantages for coping with complexity since the models are platform independent. They can be decomposed to be developed independently by experts of the respective fields, and they are highly reusable and may be subjected to formal analysis. Typically, behavior is defined as the occurrence of an action, a pattern over time, or any change in or movement of an object. In systems studies, there are many different approaches to modeling behavior, such as grounding behavior simultaneously on state transitions, natural language, and flowcharts. These different descriptions make it difficult to compare objects with each other for consistency. This paper attempts to propose some conceptual preliminaries to a definition of behavior in software engineering. The main objective is to clarify the research area concerned with system behavior aspects and to create a common platform for future research. Five generic elementary processes (creating, processing, releasing, receiving, and transferring) are used to form a unifying higher-order process called a thinging machine (TM) that is utilized as a template in modeling behavior of systems. Additionally, a TM includes memory and triggering relations among stages of processes (machines). A TM is applied to many examples from the literature to examine their behavioristic aspects. The results show that a TM is a valuable tool for analyzing and modeling behavior in a system.