In the traditional approach for the evaluation of data integration queries, heterogeneous data in data sources are converted into the global data model by wrappers before being delivered to algebraic operators. Consequently, query execution plans (QEPs) are composed exclusively by operations in accordance to the global data model. This work proposes a new data integration query evaluation strategy, named Moving Wrappers, in which data conversion is considered as an operation placed in any part of the QEP, based on a query optimization process. This permits the use of algebraic operators of the data sourceís data model. So, a QEP may include fragments with operations in different data models converted to the global data model by inter-algebraic operators. Based on this strategy, a query execution engine (QEE), named RXQEE (Relational-XML Query Execution Engine), was developed as an instance of QEEF (Query Execution Engine Framework). In particular, RXQEE explores integration queries over Relational and XML data, and therefore it implements algebraic operators, in XML and Relational models, and inter-algebraic operators, permiting the execution of integration QEPs.