We study tree languages that can be defined in Δ ₂. These are tree languages definable by a first-order formula whose quantifier prefix is , and simultaneously by a first-order formula whose quantifier prefix is , both formulas over the signature with the descendant relation. We provide an effective characterization of tree languages definable in Δ ₂. This characterization is in terms of algebraic equations. Over words, the class of word languages definable in Δ ₂ forms a robust class, which was given an effective algebraic characterization by Pin and Weil [11].