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This paper describes an execution model being developed for distributed object-oriented in a message-passing multiple-instruction/multiple-data-stream (MIMD) environment. The objective is to execute an object-oriented program as concurrently as possible. Some opportunities for concurrency can be identified explicitly by the programmer. Others can be identified at compile time. There are some opportunities for concurrency, however, that can only be discovered at runtime because they are data-dependent. The model of execution we describe attempts to discover and exploit the data-dependent concurrency that exists in a given program execution.