Increased electric power consumption causes transmission lines to be driven close to or even beyond their transfer capacities resulting in overloaded lines and congestions. Flexible AC Transmission Systems (FACTS) provide an opportunity to resolve congestions by controlling power flows and voltages. The focus in this paper lies on the Thyristor Controlled Series Compensator (TCSC) and the Static Var Compensator (SVC) as they are already in use.In general, SVCs and TCSCs are controlled locally without any coordination. The resulting mutual influences may lead to a suboptimal control performance which may endanger the security of the system. In simulations where SVCs and TCSCs are controlled by local PI controllers with anti-windup, the interactions among the devices are demonstrated with TCSCs in parallel lines as well as in nonparallel lines, SVCs at different buses and a combination of TCSC and SVC in the same grid. It is shown how the controllers interact with each other, in the worst case ending up in an unsolvable conflict.Finally, a supervisory control based on optimal power flow is developed coordinating the actions of the FACTS devices placed in the same grid such that conflicts among devices are prevented. The objective is to ensure secure transmission of electrical power and to avoid congestions resulting in overloaded and possibly disconnected lines. In a test grid, the improvements in active power losses, in line loadings and in voltage profile are demonstrated.