This abstract accompanying a presentation at S+SSPR 2006 explores the use of Support Vector Machines (SVMs) for predicting structured objects like trees, equivalence relations, or alignments. It is shown that SVMs can be extended to these problems in a well-founded way, still leading to a convex quadratic training problem and maintaining the ability to use kernels. While the training problem has exponential size, there is a simple algorithm that allows training in polynomial time. The algorithm is implemented in the SVM-Struct software, and it is discussed how the approach can be applied to problems ranging from natural language parsing to supervised clustering.