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In services and cloud computing, processes need to be continually adapted to changing environments and requirements. Undisciplined process adaptation could easily lead to data flow anomalies, e.g., input missing for some activities in the process. In this paper, we study the problem of data-flow-correctness-preserving adaptation and propose three important criteria that can maintain the data flow correctness in process adaptation. We demonstrate our approach by using a typical process adaptation scenario in BPEL.