This thesis explores the subject of automatic verification of product line models. This approach is based on the hypothesis that to automatically verify product line models, they should first be transformed into a language that makes them computable. In this thesis, product line models are transformed into constraint (logic) programs, then verified against a typology of verification criteria. The typology enumerates, classifies and formalizes a collection of generic verification criteria, i.e. criteria that can be applied (with or without adaptation) to any product line formalism. The typology makes the distinction between two categories of criteria: criteria that deal with the formalism in which models are represented, and the formalism-independent criteria. To identify defects in the first category, the thesis proposes a conformance checking approach directly related with verification of the abstract syntactic aspects of a model. To identify defects in the second category, the thesis proposes a domain-specific verification approach. An optimal algorithm is specified and implemented in constraint logic program for each criterion in the typology. These can be used independently -or in combination- to verify individual product line models. The thesis offers to support the verification of multiple product line models using an integration approach. Besides, this thesis proposes a series of integration strategies that can be used before applying the verification as for individual models. The product line verification approach proposed in this thesis is generic in the sense that it can be reused for any kind of product line model that instantiates the generic meta model based on which it was developed. It is general in the sense that it supports the verification of a comprehensive collection of criteria defined in the typology. This approach was implemented in a prototype tool that supports the specification, transformation, integration, configuration, analysis and verification of product line models via constraints (logic) programming. A benchmark gathering a corpus of 54 product line models was developed, then used in a series of experiments. The experiments showed that (i) the implementation of the domain-specific verification approach is fast and scalable to product line models up-to 2000 artefacts; (ii) the implementation of the conformance checking approach is fast and scalable to product line models up-to 10000 artefacts; and (iii) both approaches are correct and useful for industrial-size models.