This paper presents a framework governing multiple state machines (SMs) to generate behaviors for kinematically-coupled multi-arm robots. A SM is one of the most used tools to switch controllers in robotics, however, it represents only one motion at a certain time. Such a limit of representation not only restricts the potential of the kinematical redundancy but also significantly increases the number of situations we have to consider in behavior design. To relax the problem, this paper provides a distributed design scheme and an online synthesis method for SMs. The base of the framework is a task-priority-based control method for redundant robots. We expand it by introducing an abstract data structure specialized in robotic behaviors. The abstract reformulation naturally connects with SMs so that the framework realizes parallelism of sequential logic. A priority queue constructed in each control loop integrates SMs designed for each effector, and the framework automatically generates whole-body behaviors online. In dynamic simulations, the framework governs four SMs and achieves reaching tasks with a dual-arm manipulator at 1 kHz. It is shown that the loose coupling of the SMs yields reactive and flexible decisions in a dynamic environment.