One of the main difficulties with configuration problem solving lies in the representation of the domain knowledge because many different aspects, such as taxonomy, topology, constraints, resource balancing, component generation, etc., have to be captured in a single model. This model must be expressive, declarative, and structured enough to be easy to maintain and to be easily used by many different kind of reasoning algorithms. This paper presents a new framework where a configuration problem is considered both as a classification problem and as a constraint satisfaction problem (CSP). Our approach deeply blends concepts from the CSP and object-oriented paradigms to adopt the strengths of both. We expose how we have integrated taxonomic reasoning in the constraint programming schema. We also introduce new constrained variables with nonfinite domains to deal with the fact that the set of components is previously unknown and is constructed during the search for solution. Our work strongly focuses on the representation and the structuring of the domain knowledge, because the most common drawback of previous works is the difficulty to maintain the knowledge base that is due to a lack of structure and expressiveness of the knowledge representation model. The main contribution of our work is to provide an object-oriented model completely integrated in the CSP schema, with inheritance and classification mechanisms, and with specific arc consistency algorithms.