In order to efficiently compute Fast Fourier transform (FFT) various parallel algorithms and their implementation to multiprocessors and multicomputers have been developed. In general, the local interconnection network is more high speed than a global one, but its capability depends on network architecture. On the other hand, the global interconnection network is not so high speed, but it does not depends on network architecture. It provides a flexible communication interface to the programmer. In this paper, we discuss parallel radix R FFT algorithms on a multiprocessor or multicomputer system with a global interconnection network. We propose two algorithms a stage-by-stage method and a multi-stage method. We also estimate the communication time. Then we show that the communication time is very sensitive to and affected by data exchange strategy. Finally, we implement these algorithms on two commercial massively parallel computers(nCUBE/2 and CM5) and measure these communication time.