This study uses a spatial-temporal model to analyze the spatial spread of the AIDS epidemic (adult cases) in the municipality of Rio de Janeiro, Brazil, during three periods: 1988-1990, 1991-1993, and 1994-1996. City districts were used as the geographic units of analysis. A spatial analysis was also performed for pediatric AIDS cases due to vertical HIV transmission, according to period of birth, 1985-90 and 1991-96. For total adult AIDS cases, the initial period was characterized by a polygonal cluster located around the harbor area, which expanded from west to east. Among homosexual cases, in situ growth predominated, and a decrease in the intensity of the diffusion process was observed from the second to the final period. Among heterosexual cases, the epidemic displayed a relevant geographic spread, mainly from 1988-1990 to 1991-1993. Among female cases in the final time period, a cluster of high incidence rates was found towards the northwest, including very poor areas. Among pediatric cases in 1991-1996, a significant correlation was found between AIDS incidence rates and poverty levels in the respective municipal districts. The results suggest that a more complete understanding of AIDS spatial-temporal dynamics can make a major contribution to preventive measures.