The discontinuation of smallpox vaccination will lead to a gradual decrease or disappearance of immunity to poxviruses of the genus Orthopoxvirus. It is discussed whether orthopoxviruses of animals may then constitute a potential danger to man, with respect to their mutagenic and adaptation capabilities as well as their possible genetic interactions. Infection of man with these viruses is generally possible, but at present, not of acute importance. Monkeypox and cowpox viruses, as well as their variants occurring in carnivores and rodents, are of primary interest for individuals who have not been vaccinated against smallpox. Suggestions are put forward on how the human population, as well as domestic and laboratory animals, may be protected against infection with orthopoxviruses originating from animals. In particular, it is recommended that endangered groups of people should receive voluntary vaccination with genetically stable, attenuated vaccinia virus strains.