Model-based diagnosis is the activity of locating malfunctioning components of a system solely on the basis of its structure and behaviour. Diagnostic systems usually rely on qualitative models and reason by local constraint propagation methods. However, there is a large class of applications where ATMS-like systems or pure logic programs are unpractical since they are unable to solve simultaneous equations. In particular, modeling real-valued system parameters with tolerances requires some degree of numerical processing, and feedback loops in general cannot be resolved by local constraint propagation methods. Examples of such systems are analogue circuits, e.g., amplifiers or filters. In the paper we describe the role of Constraint Logic Programs over the domain of reals (CLP(R)) in representing both, qualitative and numerical models. CLP(R) is a logic programming system extended with solver for systems of linear equations and inequalities over real-valued variables.