In this paper we present the elements of an algorithmic debugger for XQuery. Given a XQuery program/query, a debugging tree is built in which the root is the query and the answer, and non-root nodes contain the results of function calls and XPath expressions computed from the query. Using the higher-order capabilities of XQuery several navigation strategies can be defined, enabling the adaptation of the debugging to the program/query and the user needs. Debugging trees and concepts as (partially) incomplete and incorrect answers are formally defined for queries in terms of XQuery semantics. A Web tool has been developed allowing the visualization of the debugging tree and the debugging of a XQuery program/query with the selected navigation strategy.