In order to estimate the cumulative number of adults infected with Human Immunodeficiency Virus (HIV) in France, the method of "backcalculation" was applied. This method assumes that the incubation period is constant over time, but the therapies administered since May 1987 among Acquired Immunodeficiency Syndrome (AIDS)-free HIV seropositive, extend the incubation period. It is obvious that if AIDS incidence counts beyond June 1987 are included in the backcalculation, this may lead to underestimation of the number of HIV infected subjects. For this reason we focused our study on estimates obtained from AIDS cases diagnosed until June 30, 1987. For each estimate we made the hypothesis of an average incubation time of 11 years (i.e. period between time of infection and onset of AIDS). We also examined the sensitivity of the results, with distributions of average incubation periods of 9 to 13 years. A "plausible range" (PR) was systematically calculated: it takes into account the imprecisions arising from model adjustment and from uncertainties regarding distribution of incubation period. Thus, the total number of infected people in France up to June 30, 1987, was estimated at 142,300 (PR: 82,200 to 240,600), corresponding to an infection rate of 0.42 (PR: 0.24% to 0.71%) for the population between 15 and 59 years of age. Estimations were also calculated according to sex for some transmission groups: homosexuals, injecting drug users and heterosexuals.