The mathematical modeling of the dynamics of autoimmune diseases contributes to the understanding of their mechanisms, thus providing better guidance for treatments. In this context, this thesis analyzes a distributed delay differential equations system modeling the evolution of HIV in an infected body, describing the interactions between uninfected CD4-T cells, infected cells, virus particles and the immune response. Aavani [1] studied a similar but simpler model, incorporating a discrete delay, which we generalize using alternative methods for the investigation of stability of stationary solutions. The asymptotic behavior of the solutions is entirely characterized by the delay, denoted \(\tau \) , representing the time before an infected cell produces virus particles. It is shown that for a sufficiently large value of \(\tau \) , i.e. above a certain threshold \(\tau_1 \), the infection tends to die out since the disease-free steady-state is asymptotically stable. Then, for a delay below this threshold, the infection persists : the disease-free steady-state being unstable. In this case, the acute steady-state and the chronic stage exchange asymptotic stability according to another threshold \(\tau_2 \). Numerical simulations finally support the conclusions obtained analytically.