A method for checkpointing a multithreaded application program, based on the egalitarian and competitive active replication strategy. The invention enables different threads to be checkpointed at different times in such a way that the checkpoints restore a consistent state of the threads at a new or recovering replica, even though the threads operate concurrently and asynchronously. Separate checkpoints are generated for the local state of each thread and for the data that are shared between threads and are protected by mutexes. The checkpoint of the shared data is communicated in a special message that also determines the order in which the claims of mutexes are granted to the threads. A source-code preprocessor tool is described for inserting code into an application program to checkpoint the state of the thread during normal operation and to restore the state of the thread from the checkpoint subsequently.