The problem of concurrent markup hierarchies in XML encodings of documents has attracted attention of a number of humanities researchers in recent years. The key problem with using concurrent hierarchies to encode documents is that markup in one hierarchy is not necessarily well-formed with respect to the markup in another hierarchy. Previously proposed solutions to this problem rely on the XML expertise of the editors and their ability to maintain correct DTDs for complex markup languages. In this paper, we approach the problem of maintenance of concurrent XML markup from the Computer Science perspective. We propose a framework that allows the editors to concentrate on the semantic aspects of the encoding, while leaving the burden of maintaining XML documents to the software. The paper describes the formal notion of the concurrent markup languages and the algorithms for automatic maintenance of XML documents with concurrent markup.