In long running parallel computations it may sometimes behelpful to migrate individual threads from one machine to another. Thishas applications in fault tolerance as well as runtime performance. However, a typical parallel application will rely on a certain globalstate that may no longer exist once migration has occured. Furthermore,it may be advantageous to migrate a thread to a heterogeneousarchitecture. How can a consistant global state be maintained in such asituation? Here we discuss the data conversion and consistency issuessurrouding heterogeneous thread migration. We show that this can beaccomplished in a method that is completely transparent to theuser/programmer.