Between 1978 and 1980 a cohort of approximately 6700 homosexual and bisexual men were recruited from the San Francisco City Clinic to participate in studies of sexually transmitted hepatitis B. Testing frozen blood specimens collected at intervals from these patients provides a means of tracking the spread of the AIDS virus since 1978. The rate of spread of HIV was estimated by fitting different survival curves to interval-censored serological data using maximum likelihood techniques. The curves were compared using the Akaike Information Criterion (AIC) to select that which best describes the data. The best was found to be a log-logistic model, which suggested that between 1978 and 1981 the virus spread rapidly, infecting 44% of the then uninfected cohort members. More recently the rate of spread has declined, with an additional 32% of the cohort becoming infected between 1981 and 1987.