Acephalous in acephalous society literally means headless, that is, the society is without any formalized or institutionalized system of power and authority. In a acephalous society, collective decisions are made in a variety of ways, including informal gatherings. Acephalous society is also known as egalitarian or non-stratified society. Related to acephalous society concept are monocephalous (one leader, as in a monarchy) and polycephalous, where the society operates as a number of independent units, each having a leader but all representing the society as a whole. Many anarchist and libertarian socialist societies that have abolished social inequality are also considered acephalous societies. Certain nomadic societies are also distinguished as acephalous societies.
The non-stratified organization of society of indigenous peoples - Indigenous Peoples in Asia - by Gerald Faschingeder. Although some of these peoples today consist of some million members, indigenous peoples usually are smaller groups that count no more than some hundred thousand members. Many peoples are acephalous societies, so to say "politically headless", which does not mean that there is a lack of political concepts, but that they do not know a highest leading person. Rather, they are segmentarily organized, i.e. they consist of several similar parts or "segments" that are equal in rank, and these segments may subdivide into sub-segments of various sizes. So, these societies are not disorganized or without structures, as the former term "primitives" implied. Of course, they know social differentiation and hierarchy, but nevertheless, there is less division of labor to be found than in non-indigenous societies.
Although the acephalous society or segmentary organization cannot be presented as universal principle of all indigenous societies, this comment indicates why most of the indigenous societies were not and are not easily compatible with non-indigenous ones.
Indigenous societies do have specific cultural characteristics, but their common features cannot be reduced to a single criterion. Kuppe, for example, mentions three central points of this topic: "a close relationship between these societies and their lebensraum, a lack of organization as state and social stratification, and the dealing with conflicts within a society that is not based on institutional force by the state." (Kuppe 1990:10).