We consider distributed-memory parallel machines that support the FIFO
delivery of messages among processors, and present an asynchronous di
stributed algorithm that ensures the FIFO delivery of messages among t
asks that migrate in such machines. For the concurrent migration of a
set K of tasks, the algorithm requires O(nm(K)) interprocessor message
s and O(n) time to run, where n is the number of processors in the sys
tem and m(K), is the number of pairs of communicating tasks involving
the migrating tasks. However, for a great number of current distribute
d-memory architectures, these complexities can be reduced to O(m(K)) a
nd O(1), respectively.