Abstract: The development of concurrent object\|oriented programming languages has suffered from the lack of a widely accepted formal foundation for describing the semantics of concurrent object systems. Based on the \|calculus and the actor model respectively, attempts have been made to define a common semantic framework for concurrent object\|oriented programming. By compromising these two approaches, a formalism that enjoys a clean formal definition is defined, which allows the reuse of standard results of the theory of concurrency, while preserving a high level object\|oriented programming style. The actor algebra and the concurrent object calculus are proposed in the paper here, and the translation relationship between the two approaches is also presented.