Projections of the spread of the acquired immunodeficiency syndrome (AIDS) and of its etiologic agent, the human immunodeficiency virus (HIV), are presented for homosexual/bisexual men and intravenous drug users in the five European countries with the largest caseloads. The results suggest that the HIV epidemic for French, German, and British homosexual/bisexual men has peaked around 1985 and declined rapidly thereafter. By the end of the century, and for a median incubation period m of AIDS equal to 8 years, the total numbers infected in these groups are predicted to be about 31,000, 15,000, and 9,000, respectively. (These estimates more than double if m is taken equal to 12 years). The results suggest that the HIV epidemic among Italian and Spanish intravenous drug users (IVDUs) peaked in 1986 and also decreased rapidly thereafter. For an assumed median incubation period m of 8 years, the total number of infected IVDUs by the end of the century is predicted to be about 22,000 and 16,000 in Italy and Spain, respectively. (Again, these estimates more than double if m is taken equal to 12 years.) The projections suggest that in the late 1980s or early 1990s the annual incidence of AIDS cases among IVDUs in Spain and Italy will overtake the incidences of homosexual/bisexual AIDS cases in the Federal Republic of Germany and the United Kingdom. In all cases the annual incidence of AIDS will reach its maximum in the early to mid 1990s. However, the AIDS epidemic will be protracted because of the long incubation period