The following classes of connecting networks, based on their combinatorial properties, have been previously defined: networks nonblocking in the strict sense, networks non blocking in the wide sense, rearrangeable networks, and blocking networks. In this paper we add the class of repackable networks, i.e., networks in which blocking can be avoided by using call repacking control algorithms. The conditions under which a three-stage Clos network is repackable are formulated and proved. The numbers of middle-stage switches in all network classes are compared as well the differences between repackable and rearrangeable networks are discussed.