The paper introduces mixed networks, a new graphical model framework for expressing and reasoning with probabilistic and deterministic information. The motivation to develop mixed networks stems from the desire to fully exploit the deterministic information (constraints) that is often present in graphical models. Several concepts and algorithms specific to belief networks and constraint networks are combined, achieving computational efficiency, semantic coherence and user- interface convenience. We define the semantics and graphical representation of mixed networks, and discuss the two main types of algorithms for processing them: inference-based and search-based. A preliminary experimental evaluation shows the benefits of the new model.