Inductive Logic Programming (ILP) is concerned with learning hypotheses from examples, where both examples and hypotheses are represented in the Logic Programming (LP) language. The application of ILP to problems involving numerical information has shown the need for basic numerical background knowledge (e.g. relation “less than”). Our thesis is that one should rather choose Constraint Logic Programming (CLP) as the representation language of hypotheses, since CLP contains the extensions of LP developed in the past decade for handling numerical variables. This paper deals with learning constrained clauses from positive and negative examples expressed as constrained clauses. A first step, termed small induction, gives a computational characterization of the solution clauses, which is sufficient to classify further instances of the problem domain. A second step, termed exhaustive induction, explicitly constructs all solution clauses. The algorithms we use are presented in detail, their complexity is given, and they are compared with other prominent ILP approaches.