GATTAL, Wiam2024-09-292024-09-292024-06-08http//localhost:8080/jspui/handle/123456789/12003In this thesis, we address the issue of time delays that commonly appear in ordinary differen tial equations (ODEs). The purpose of this thesis is to explore the types of problems that cannot be solved by ODEs and require delay differential equations (DDEs) for their solution. We will also study some of the key results of DDEs that correspond to their counterparts in ODEs, with a particular focus on DDEs with constant delay. Additionally, we will discuss the concept of stability in delayed differential equations DDEs.enDifferential equations with time delay, (DDEs), Stability, Existence and uniqueness of solutions, Constant delay.Thesis