A data processing system allows processes to be checkpointed and restarted. The system saves the old process and thread identifications in a process table. When an application makes a system call passing the old process and/or thread identifications as parameters, the system performs a mapping algorithm to supply the system call with the new process and/or thread identifications. When a system call returns a new identification, the system performs a remapping algorithm to return the old identifications to the calling application program. When a group of process is restarted for which the process group leader was not checkpointed, the system creates a ghost process group leader.