Summary: We present a model for distributed logic programming based on AND- parallelism and on explicit message-passing primitives. The communication mechanism is inspired by \textit{R. Milner}'s CCS [Lect. Notes Comput. Sci. 92 (1980; Zbl 0452.68027)]. First, a simple calculus of communicating sequential logic processes is defined to formally introduce this notion of communication in a logic programming setting. Then, the definition of the language is completed by extending the calculus with an alternative command, as well as with mechanisms for the dynamic creation of AND- parallel processes. The resulting language is a variant of Distributed Logic defined by \textit{L. Monteiro} [A Proposal for distributed Programming in Logic, in: Implementations of Prolog, Ellis Horwood, 329--340 (1984)]. The second part of the paper focuses on the study of the semantics of the language. We define a model-theoretic semantics by providing the various goal composition operators and the communication primitives with a clear logical meaning. On the other hand, an operational semantics is given in terms of the distributed model of Petri nets. The latter characterization is shown to provide several insights on the programming language, such as the ability of capturing fairness and liveness properties. The study of the semantics terminates with the proof of the equivalence (soundness and completeness) between the model-theoretic and the operational semantics.