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In this paper, the Multi-flow Asynchronous Temporal Logic, called MAT Logic, is presented. MAT Logic is a new temporal×modal logic with non-deterministic operators among time flows as accessibility relations. The main goal of this work has been the design and description of a logic that could be capable of managing communications among systems with not necessarily synchronizable time flows. In order to better understand the design of the logic, an example in the field of communications is given.