A study is made of the problem of designing low complexity control algorithms for controlling three-stage connecting networks with the objective of improving system performance. The chosen approach is based on the theory of connecting networks and makes use of rearrangement algorithms. These algorithms are applicable to a number of environments, including multipoint connections, time plan modifications in satellite systems, and real-time routing. The main feature of the algorithms is an asynchronous mode of operation for modifying the system switching configurations. A theoretical framework has been developed for defining the conditions that must hold for the asynchronous rearrangements to work. A quantitative evaluation of these algorithms obtained with a computer simulation program is given.>