In this paper, we discuss kernels that can be applied for the classification of XML documents based on their DOM trees. DOM trees are ordered trees in which every node might be labeled by a vector of attributes including its XML tag and the textual content. We describe five new kernels suitable for such structures: a kernel based on predefined structural features, a tree kernel derived from the well-known parse tree kernel, the set tree kernel that allows permutations of children, the string tree kernel being an extension of the so-called partial tree kernel, and the soft tree kernel. We evaluate the kernels experimentally on a corpus containing the DOM trees of newspaper articles and on the well-known SUSANNE corpus.