The study of node-selection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as first-order logic (FO) or monadic second-order logic (MSO), have been considered. Results in this area typically relate an Xpath-based language to a classical logic. What has yet to emerge is an XPath-related language that is expressive as MSO, and at the same time enjoys the computational properties of XPath, which are linear query evaluation and exponential query-containment test. In this paper we propose µXPath, which is the alternation-free fragment of XPath extended with fixpoint operators. Using two-way alternating automata, we show that this language does combine desired expressiveness and computational properties, placing it as an attractive candidate as the definite query language for trees.