In this talk we introduce a model for the dynamics of HIV epidemics under distinct HAART regimes, and study the emergence of drug-resistance. The model predicts HIV dynamics of untreated HIV patients for all stages of the infection. We compute the local and the global stability of the disease-free equilibrium of the model. We simulate the model for two distinct HIV patients, the rapid progressors and the long-term non- progressors. We study the effects of equal RTI and PI efficacies, as well as distinct drug efficacies, namely RTI-based and PI-based therapeutics. Treatment is initiated when the CD4+T cells count is less than 350 cells mm-3. ThePI-based drugs seem to produce better outcomes, with respect to disease progression, than RTI-based regimes.