The models presented are discrete Monte Carlo(MC) and Cellular Automata(CA) representations of the interaction of HIV with the immune system. HIV is characterised by the depletion of Helper T cells in the body. Helper T cells are essential to the correct regulation of the immune system. Their degradation leaves the body incapable of defending itself, even against what is usually an unharmful infection. The models consider just four cell types the Macrophage, M, the helper T cell, H , the cytotoxic Killer cell, C and the virus, V. Each cell type can either be in high concentration (1) or low concentration (0). An up d a te of a site consists of nearest-neighbour interaction followed by intra-site interactions. The nearest-neighbour interaction represents the influence of a site’s surroundings on it. The intra-site interactions are Boolean equations which represent a succinct interpretation of HIV infection and its effect on the host immune system. Mutation is considered via a probabilistic parameter P m u t - Each cell type has inherent mobility due to the nearest-neighbour interactions, explicit mobility is explored by a probabilistic parameter Pmob• The MC and CA .simulations differ in their updating, with CA updating is synchronous and with MC it is asynchronous. MC is explored as an alternative to the CA model form. Due to th e Boolean concentrations of the cell types, synchronous (CA) updating leads to overshooting, there is either complete viral dominance or immune dominance and no intermediate state. Asynchronous (MC) updating smoothes these extremes; intermediate states between immuno-dominance and immuno-deficiency exist. These intermediate states offer new insight into the dynamics of HIV and the immune system. Asynchronous updating gives clearly defined growth patterns and this enables th e exploration of critical points. One such critical point is the value of Pmut for which the cross-over between immune dominance and deficiency occurs. Also characteristics of the disease progression such as latency can be investigated.