Execution control is a critical task of robot architectures which has a deep impact on the quality of the final system. In this study, we describe a general method for execution control, which is a part of the Aerostack software framework for aerial robotics, and present technical challenges for execution control and design decisions to develop the method. The proposed method has an original design combining a distributed approach for execution control of behaviors (such as situation checking and performance monitoring) and centralizes coordination to ensure consistency of the concurrent execution. We conduct experiments to evaluate the method. The experimental results show that the method is general and usable with acceptable development efforts to efficiently work on different types of aerial missions. The method is supported by standards based on a robot operating system (ROS) contributing to its general use, and an open-source project is integrated in the Aerostack framework. Therefore, its technical details are fully accessible to developers and freely available to be used in the development of new aerial robotic systems.