The properties of switching techniques suitable for use in broadband networks have been investigated. Methods for evaluating the performance of such switches have been reviewed. A notation has been introduced to describe a class of binary self-routing networks. Hence a technique has been developed for determining the nature of the equivalence between two networks drawn from this class. The necessary and sufficient condition for two packets not to collide in a binary self-routing network has been obtained. This has been used to prove the non-blocking property of the Batcher-banyan switch. A condition for a three-stage network with channel grouping and link speed-up to be nonblocking has been obtained, of which previous conditions are special cases. A new three-stage switch architecture has been proposed, based upon a novel cell-level algorithm for path allocation in the intermediate stage of the switch. The algorithm is suited to hardware implementation using parallelism to achieve a very short execution time. An array of processors is required to implement the algorithm The processor has been shown to be of simple design. It must be initialised with a count representing the number of cells requesting a given output module. A fast method has been described for performing the request counting using a non-blocking binary self-routing network. Hardware is also required to forward routing tags from the processors to the appropriate data cells, when they have been allocated a path through the intermediate stage. A method of distributing these routing tags by means of a non-blocking copy network has been presented. The performance of the new path allocation algorithm has been determined by simulation. The rate of cell loss can increase substantially in a three-stage switch when the output modules are non-uniformly loaded. It has been shown that the appropriate use of channel grouping in the intermediate stage of the switch can reduce the effect of non-uniform loading on performance.