The ROL system is a novel deductive object-oriented database system that has been implemented at the University of Regina. It provides a uniform rule-based declarative language for defining, manipulating and querying databases, which integrates important features of deductive databases and object-oriented databases. It supports object identity, complex objects, classes, class hierarchies, multiple inheritance with overriding and blocking, and schema definition. It also supports structured values such as functor objects and sets, treating them as first class citizens, and providing powerful mechanisms for representing both partial and complete information about sets. This paper describes the query processing mechanism in the ROL system. A novel feature is that it effectively combines the top-down and bottom-up strategies and automatically decides which evaluation strategies to use based on the nature of the query and data in the databases.