The group favouring apartheid is either a minority population or about to become a minority population. Apartheid isn't the sort of strategy adopted by the majority population of a delimited and secure territory. Similar policies can be and have been adopted towards unpopular groups of immigrant background and other indigenous minorities, ranging from forced assimilation to genocide, but the similarity is only superficial. These strategies are generally designed to prevent the dominant group's contamination, to avoid its adulteration. Apartheid is a last-ditch defense of a threatened position that liberal individualism will insidious destroy.
The group favouring apartheid believes itself to be indigenous. The myth of indigeneity is critically importance for any apartheid mythology. The group in question believes itself to be the rightful proprietor of its own territory, to be descended from the first people ever to effectively occupy that piece of land. This indigeneity trumps the collective rights of other groups on that territory, just as it denies the individual rights of people who don't belong to the "indigenous" population.
The group favouring apartheid believes that it must act immediately. Apartheid is a strategy that appeals to those groups which see themselves as threatened, whether by a relatively benign assimilation or by destruction. Nothing can be allowed compromise the indigenes ' presence in their homeland; no more ground can be given without threatening the group's very existence.
Under apartheid, each group must develop separately. Proponents of apartheid systems don't believe in such things as porous group boundaries. If they did, perhaps they might be more sanguine about the viability of multicultural societies. The group's territory must be defended, but this is only one element of an all-out effort intended to prevent the assimilation of the group. Individuals from different groups cannot be allowed to collaborate, not even if they want to. All the connections uniting people of different backgrounds in non-apartheid societies--cultural, economic, political, personal--must be severed immediately. The only sorts of connections permissible are those which don't challenge the apartheid system.
The group behind the apartheid system must establish as complete a monopoly over power as possible. Some powersharing is possible with influential groups capable of posing a direct threat to the system, usually in the economic realm, but the group favouring apartheid must dominate the state. No one can be allowed to threaten the system. Separate development can be made to reinforce this goal, by limiting the development of the actual or imminent majority into a population capable of replacing the group benefiting from apartheid.
Defending the apartheid system requires constant vigilance. The marginalized population(s) within the apartheid state's frontiers, and hostile populations outside the borders, must be kept from challenging the system. Where possible, propaganda is used, perhaps borrowing from the rhetoric of Wilsonian self-determination, making claims about historically specific patterns of development, or arguing from necessity. Where propaganda fails, the coercive power of the state must be applied, up to and including the use of military force.
Consider the prototypical apartheid state of South Africa, if you will. Afrikaners, fearful not only of the growth of South Africa's Anglo population though immigration but the prospect of an enfranchised non-white population, instituted apartheid in order to build an Afrikaner nation-state immediately after the Second World War. Anglos, and to a limited extent Indians and Coloureds, were brought into the new structures of power in economic roles; Afrikaners dominated the political and military portions of the South African state. At great human cost, as I wrote last year, each major population group was forced to develop separately under unpromising conditions, fragmented, with as little resources as possible, and serving the dominant population. This system was fragile, and had to be defended by wars against South Africa's neighbours, the imposition of a full-fledged police state at home, and an active campaign of foreign propaganda seeking to position South Africa as a bastion of anti-Communism.
This isn't a definitive list by any means, and I can imagine some points where it could break down. What about empires directly integrated with their metropoles? What about multiethnic countries like the former Socialist and Federal Republic of Yugoslavia? Even so, it's safe to say that the necessary preconditions for an apartheid system are the identification of an existential threat facing a particular population and the belief that a liberal-individualist model will destroy this population. Only illiberal and destructive policies can prevent this threat from coming to fruition.
UPDATE (10:49 PM) : Crossposted at GNXP.