The current project proposes the comparison of two pharmacologic strategies as adjunctive treatments for the improvement of HIV-associated neurocognitive disruption, additionally to use of HAART. The investigators propose the use of the compound that has shown greatest benefits in this context to date, the lithium, versus the use of a well-tolerated and promising drug in other pathologies with neurocognitive affectation, such as Alzheimer or Parkinson diseases, which is the rivastigmine. In those other diseases, this second compound has recently offered a good tolerability, but also benefits on attention, memory and other neurocognitive areas. Both study groups, patients on therapy with lithium and patients on therapy with rivastigmine, will be compared to a control group, which will not initiate any other treatment (therefore only continuing antiretroviral therapy). The investigators are aware that this proposal will offer new relevant data for the study of neurocognitive improvement in HIV infection, as well will allow a better knowledge of clinical management of HIV-infected patients with CNS disease, an aspect that is a common clinical concern today.