The question of sustainability of agricultural production especially animal production and events leading to its development can be dated back to the second part of the last century. Sustainability is a priority subject matter as it is a core element in our existence and in the survival of the forthcoming generations. The notion of sustainability comprises three aspects: ecological, social and political and economic target systems, which by now have been supplemented with cultural and regional elements including the protection of environment, local traditions, scale of values, cultural and historical heritage. The principles of sustainable development also include the improvement of human and animal health and the maintenance of vital rural communities. The priority notion of sustainability of agricultural production refers also to animal husbandry and especially sheep production. Sheep have contributed substantially to the grassland-based agricultural production in Hungary for centuries. Sheep sector is important in rural areas as the tool of sustainability of animal production. It should also be highlighted that contrary to numerous efforts, the globally difficult process of sustainable development poses almost unsolvable problems for implementers even on local and regional levels. This paper will review briefly the levels of sustainability in the Hungarian animal production with a special regard to sheep production and their content and then points out the most significant economic issues by the application of “SWOT” – analysis, “problem tree’and “structure of objectives” methods, on the grounds of the received findings.