Path constraints have been studied in [3, 8, 9] for semi-structured data. In this paper, we investigate path constraints for structured data. We show that there is interaction between path constraints and type constraints. In other words, results on path constraint implication in semistructured databases may no longer hold in the presence of types. We also investigate the class of word constraints for databases of two practical object-oriented data models. In particular, we present an abstraction of the databases in these models in terms of first-order logic, and establish the decidability of word constraint implication in these models.