Frequent structure mining (FSM) aims to discover and extract patterns frequently occuring in structural data, such as trees and graphs. FSM finds many applications in bioinformatics, XML processing, Web log analysis, and so on. In this paper we present a new FSM technique for finding patterns in rooted unordered labeled trees. The patterns of interest are cousin pairs in these trees. A cousin pair is a pair of nodes sharing the same parent, the same grand-parent, or the same great-grandparent, etc. Given a tree T, our algorithm finds all interesting cousin pairs of T in O(|T|²) time when |T| is the number of nodes in T. Experimental results on synthetic data and phylogenies show the scalability and effectiveness of the proposed technique. To demonstrate the usefulness of our approach, we discuss its applications to locating co-occurring patterns in multiple evolutionary trees, evaluating the consensus of equally parsimonious trees, and finding kernel trees of groups of phylogenies. We also describe extensions of our algorithms for undirected acyclic graphs (or free trees).