Classification is a process that consists in two dual operations: generating a set of classes and then classifying given objects into the created classes. The class generation may be understood as a learning process and object classification as a problem-solving process. The goal of this position paper is to introduce and to make precise the notion of a classification problem in object-based representation systems, e.g. a query against a class hierarchy, to define a subsumption relation between classifications problems, and to analyze the way a classification problem can be solved with respect to a class hierarchy.