Behavior-based systems form the basis of autonomous control for many robots, but there is a need to ensure these systems respond in a timely manner. Unexpected latency can adversely affect the quality of an autonomous system's operations, which in turn can affect lives and property in the real-world. A robots ability to detect and handle external events is paramount to providing safe and dependable operation. This paper presents a concurrent version of a behavior-based system called the Real-Time Unified Behavior Framework, which establishes a responsive basis of behavior-based control that does not bind the system developer to any single behavior hierarchy. The concurrent design of the framework is based on modern software engineering principles and only specifies a functional interface for components, leaving the implementation details to the developers. In addition, the individual behaviors are executed by a real-time scheduler, guaranteeing the responsiveness of routines that are critical to the autonomous system's safe operation. Experimental results demonstrate the ability of this approach to provide predictable temporal operation, independent of fluctuations in high-level computational loads.