Abstract. Based on the recursion mechanism of the XML transformation language XSL, the document transformation language DTL is defined. First the instantiation DTLreg is considered that uses regular expressions as pattern language. This instantiation closely resembles the navigation mechanism of XSL. For DTLreg the complexity of relevant decision problems such as termination of programs, usefulness of rules and equivalence of selection patterns, is addressed. Next, a much more powstraction of XSL is considered that uses monadic second-order logic formulas as pattern language (DTLmso ). If DTLmso is restricted to top-down transformations (DTLmso d ), then a computational model can be defined which is a natural generalization to unranked trees of topdown tree transducers with look-ahead. The look-ahead can be realized by a straightforward bottom-up pre-processing pass through the document. The size of the output of an XSL program is at most exponential in the size of the input. By rest...