To seamlessly cover urban and rural areas, mountains and deserts, as well as sea and air, with high quality ubiquitous communication services, the convergence of Terrestrial Networks (TNs) and Non-Terrestrial Networks (NTNs) such as satellites is essential in beyond 5G communication systems. This paper presents the scenarios and architectures of integrated and individual network control systems for TN and NTN convergence in the control plane. The integrated network control system enables end-to-end service design, orchestration, performance monitoring, closed-loop control, and automation. It promotes interoperability in the control plane of TN and NTN domains composed of virtualization-supporting infrastructures and possibly managed by different organizations. This paper is related to ITU-T Study Group 13’s activities of standardizing fixed, mobile and satellite convergence technologies.