Thanks to their small size, high dexterity and compliance, concentric tube continuum robots (CTCRs) are well suited for tasks in constrained and tortuous environments such as minimally invasive surgery. Many real-world tasks often require collaboration of multiple manipulators necessitating dual-arm (DA) robotic systems. Leveraging the benefits of CTCRs in a dual-arm configuration, i.e. DA-CTCR, has great potential for applications in such areas. A hierarchy-based control framework is proposed to efficiently control and coordinate motions in a semi-autonomous manner for DACTCRs. This framework is validated in various assistive/motion coordination control schemes in simulation and on a real-robot prototype. Our results demonstrate that a DA-CTCR can effectively be controlled when considering the autonomous execution of multiple functionally meaningful tasks aggregated in a prioritized hierarchy. The performance of the task prioritization was clear on the real robot where, for a relative positioning task prioritized over that of a single arm, respective mean errors of 0.38mm and 0.7mm were observed.