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We discuss incremental validation of XML documents with respect to DTDs and XML schema definitions. We consider insertions and deletions of subtrees, as opposed to leaf nodes only, and we also consider the validation of ID and IDREF attributes. For arbitrary schemas, we give a worst-case n log n time and linear space algorithm, and show that it often is far superior to revalidation from scratch. We present two classes of schemas, which capture most real-life DTDs, and show that they admit a logarithmic time incremental validation algorithm that, in many cases, requires only constant auxiliary space. We then discuss an implementation of these algorithms that is independent of, and can be customized for different storage mechanisms for XML. Finally, we present extensive experimental results showing that our approach is highly efficient and scalable.