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Systems based on service-oriented architecture are called service-based systems (SBS), and comprise of computing services offered by various organizations. SBS often require their services to be composed in complex workflows to perform their high-level tasks. The users usually have certain expectations on the overall QoS (quality of service) of their workflows. Due to the highly dynamic environments of SBS, in which temporary unavailability or quality degradation of services may occur frequently and unexpectedly, monitoring and controlling the execution of workflows adaptively in SBS to satisfy users' QoS requirements is needed, and should be done in distributed and proactive manner. In this paper, a design of distributed QoS monitoring and adaptive (M/A) modules for multiple workflows in adaptive SBS (ASBS) is presented. The requirements on QoS M/A in ASBS, as well as the ASBS system architecture and the coordination protocol among software modules and services in ASBS for QoS M/A, are discussed.