The (Stream) X-Machine Testing Methodology is a complete functional testing approach to software- and hardware testing that exploits the scalability of the Stream X-Machine model of computation. Using this methodology, it is likely to identify a finite test-set that exhaustively determines whether the tested system's implementation matches its specification. This goal is achieved by a divide-and-conquer approach, in which the design is decomposed by refinement into a collection of Stream X-Machines, which are implemented as separate modules, then tested bottom-up. At each integration stage, the testing method guarantees that the tested components are correctly integrated.