Based on analysis of eleven-year intense epidemiological intervention against smallpox, a number of findings and demands ensued which should be met by an infectious disease to be included into the programme of eradication or elimination. The author mentions several episodes from the programme of smallpox eradication in which he participated as a member of a WHO team. Part of the paper is a detailed explanation of the terms eradication and elimination. The main part of the article is a characteristic of infections where the global programme of eradication or elimination is underway. At present the eradication of poliomyelitis and dracunculiasis is completed and elimination of tetanus of neonates as well as leprosy, all by the year 2000. By 2010 measles, possibly German measles and mumps should be eradicated and possibly leprosy and Chagas' disease and onchocerciasis should be eliminated. Also for other infections such as lymphatic filariasis, trachoma and non-veneric treponematoses more remote terms are given or are not yet given. Depending on the decision of WHO on the programme of global eradication, under precisely defined conditions seven other infections may be included: cysticercosis (Taenia solium), diseases caused by Haemophilus influenzae b, viral hepatitis A, rotavirus enteritis, diphtheria, whooping cough and tuberculosis. In the case of viral hepatitis B only elimination is foreseen.