Data from a cohort study of 1,637 homosexual men in Los Angeles are used to estimate the distribution of times from HIV infection to AIDS, and to detect any changes in the distribution. We find weak, but not statistically significant, evidence that the incubation period is lengthening. When the incubation period distribution is assumed not to have changed, we estimate that the proportion developing AIDS within 6 years of HIV infection is 27%, with a 95% confidence interval of (23%, 31%). However, if we assume that the incubation period distribution began to change in July 1987, then we estimate that for individuals infected in the first half of 1979, 28% develop AIDS within 6 years, and for those infected in the first half of 1983, 25% develop AIDS in 6 years. Four different hypotheses are suggested for a lengthening of the incubation period; these are a treatment hypothesis, a cofactor hypothesis, a better health care hypothesis, and a changing virus and disease hypothesis. The statistical method used is semiparametric modeling of the joint distribution of the date of infection and the incubation period for the participants in the study. These methods, although computationally intensive, are an attractive way of analyzing data from a prevalent cohort because only minimal parametric assumptions are made.