The authors generalize known results for nonblocking distribution networks (also known as generalized connection networks) to the multirate environment, where different user connections share a switch's internal data paths in arbitrary functions of the total capacity. In particular, they derive conditions under which networks due to Y.P. Ofman (1965) and C.D. Thompson (1978), N. Pippenger (1973), and J.S. Turner (1989) lead to nonblocking multirate distribution networks. The results include both rearrangeable and wide-sense nonblocking networks. The complexity of most of our nonblocking multirate networks is roughly twice that of the corresponding space division networks. The one exception has complexity that exceeds that of the corresponding space division network by a log log factor. >