A model for logic programming of real time computing systems is presented. The model is based on the process interpretation of Horn-Clause Logic and employs a non-deterministic committed-choice stream-And parallel search strategy. A real time computing system is represented as a network of communicating goals where each goal maintains its own logical clock which can be read and set by the node reduction process. The system of distributed logical clocks satisfies Lamport's correctness and distributed synchronisation conditions. The programming language is a variant of GHC to which many features are borrowed from PARLOG. Primitives to express time and timing constraints are provided. A meta-interpreter is given to describe the operational semantics of the language and the implementability of the model in the language itself. A telecommunications switching system has been specified and implemented in terms of the model presented here. It is also shown that the fairness problem has a natural solution in the proposed logical frame work. This is illustrated through a real time fair binary merge operator.