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XML has become an important medium for representing and exchanging data over the Internet. Data sources, including structural and semi-structural sources, often export XML views over base data, and then materialize the view by storing its XML query result to provide faster data access. Upon change to the base data, it is typically more efficient to maintain a view by incrementally propagating the delta changes to the view than by re-computing it from scratch. Techniques for the incremental maintenance of relational views have been extensively studied in the literature. However, the maintenance of views created using XQuery is as of now unexplored. In this paper we propose an algebraic approach for incremental XQuery view maintenance. In our approach, an update to the XML source is transformed into a set of well defined update primitives which are propagated through the XML algebra tree. This algebraic update propagation process generates incremental update primitives to be applied to the result view. Our update propagation strategy based on the XAT XML algebra and the propagation rules for individual algebra operators are given. We briefly discuss our XQuery view maintenance system implementation, and present our experiments that confirm that incremental view maintenance is indeed faster than re-computation.