Abstract. More and more data (documents) are wrapped in XML format. Mining these documents involves mining the corresponding XML structures. However, the semi-structured (tree structured) XML makes it somewhat difficult for traditional data mining algorithms to work properly. Recently, several new algorithms were proposed to mine XML documents. These algorithms mainly focus on mining frequent tree structures from XML documents. However, none of them was designed for mining infrequent structures which are also important in many applications, such as query processing and identification of exceptional cases. In this paper, we consider the problem of identifying infrequent tree structures from XML documents. Intuitively, if a tree structure is infrequent, all tree structures that contain this subtree is also infrequent. So, we propose to consider the minimal infrequent structure (MIS), which is an infrequent structure while all proper subtrees of it are frequent. We also derive a level-wise mining algorithm that makes use of the SG-tree (signature tree) and some effective pruning techniques to efficiently discover all MIS. We validate the efficiency and feasibility of our methods through experiments on both synthetic and real data.