Processor and network management have a great impact on the performance of Distributed Memory Parallel Computers. Dynamic Process Migration allows load balancing and communication balancing at execution time. Managing the communications involving the migrating process is one of the problems that Dynamic Process Migration implies. To study this problem, which we have called the Message Integrity Problem, six algorithms have been analysed. These algorithms have been studied by sequential simulation, and have also been implemented in a parallel machine for different user process patterns in the presence of dynamic migration. To compare the algorithms, different performance parameters have been considered. The results obtained have given preliminary information about the algorithms behaviour, and have allowed us to perform an initial comparative evaluation among them.