We use a staged Markov model to estimate the distribution and mean length of the incubation period for acquired immunodeficiency syndrome (AIDS) from a cohort of 603 human immunodeficiency virus (HIV) infected individuals who have been followed through various stages of infection. The model partitions the infected period into four progressive stages: (1) infected but antibody-negative; (2) antibody-positive but asymptomatic; (3) pre-AIDS symptoms and/or abnormal haematologic indicator; and (4) clinical AIDS. We also model a fifth stage: death due to AIDS. The estimated mean (median) waiting times in each stage of infection are stage 1, 2.2 (1.5) months; stage 2, 52.6 (36.5) months; stage 3, 62.9 (43.6) months; and stage 4, 23.6(16.3) months. We estimate the mean AIDS incubation period (from infection to development of clinical AIDS) as 9.8 years with a 95 per cent confidence interval of [8.4, 11.2] years. The paper also considers the estimated density function of the AIDS incubation period and the estimated survival functions for individuals in each stage of infection. This work represents one of the most complete statistical descriptions to date of the natural history of HIV infection.