This paper describes the institutional background against which invasiveness is considered with regard to livestock genetic diversity. The human-made nature and extensive spread of a few domesticated animal species for global food production is a feature of agricultural diversity that complicates the simple, negative view of invasive species. The different impacts of livestock species on natural biodiversity, of breed diversity within species, and of within-breed diversity on agricultural biodiversity are discussed. Livestock production continues to threaten natural biodiversity. The increasing demand for food of animal origin, the productivity and technology differentials, as well as the information and awareness bias, tend to favour international high-output breeds over local breeds. This will increase their 'invasiveness' in the market economy if current policy distortions continue. Several measures are proposed to control genetic erosion through uncontrolled gene flow. Countries are responsible not only for control of invasive alien species under the Convention on Biological Diversity but also for sustainable use and conservation of animal genetic resources, and for food security; they must balance trade-offs between these broad policy objectives.