Abstract : We know that some proteins can regulate the expression of genes in a living organism. The regulation of gene expression occurs through networks of regulatory interactions in a non linear way between DNA, RNA, proteins and some molecules, called genetic regulatory networks. It is becoming clear that mathematical models and tools are required to analyze these complex systems. In the course of his study on gene regulatory networks R. Thomas proposed a discrete framework that mimics the qualitative evolution of such systems. Such discrete models are of great importance because kinetic parameters are often non measurable in vivo and available data are often of qualitative nature. Then Snoussi proved consistency between the discrete approach of R. Thomas and Piecewise Linear Differential Equation Systems, which are easy to construct from interaction graph and thresholds of interactions. Our work focuses on the relationships between both approaches: we will prove a result of correspondence between the two models. Finally, we will give some short description of a Maple program which can compute a discrete path, given the ordinary differential equation and starting box.