Variability models (e.g., feature models) are a common way for the representation of variabilities and commonalities of software artifacts. Such models can be translated to a logical representation and thus allow different operations for quality assurance and other types of model property analysis. Specifically, complex and often large-scale feature models can become faulty, i.e., do not represent the expected variability properties of the underlying software artifact. In this paper, we introduce DirectDebug which is a direct diagnosis approach to the automated testing and debugging of variability models. The algorithm helps software engineers by supporting an automated identification of faulty constraints responsible for an unintended behavior of a variability model. This approach can significantly decrease development and maintenance efforts for such models.