In this report, we present an algorithm for solving {\em directly} linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie \cite{contejean94ic} for solving linear Diophantine systems of equa­tions, which is itself a generalization of the algorithm of Fortenbacher \cite{clausen89} for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, {\em i.e.} provides a (finite) description of the set of solutions, it can be implemented with a {\em bounded} stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm.