A method and implementing computer system are provided which allows for significantly improved input/output (I/O) subsystem designs in all systems which include serialized I/O transactions such as so-called Express specification systems. Transaction control methodology is implemented to improve Express design requirements for Express devices such as an Express switch, Express-PCI bridge, endpoint, and root complex. This is accomplished by utilizing improved transaction ordering and state machine and corresponding buffer design and improved flow control credit methodology which enables improved processing for controlling transactions flowing through Express devices including Express switches and Express-PCI bridges. An Express-PCI/PCIX transition bridge design is also provided, along with the flow control credit methodology and implementation within the Express-PCI/PCIX bridge design to enable efficient interfacing between Express and legacy or existing PCI/PCIX systems.