Biculturalism describes a society with two large ethnic, religious or linguistic groups, to the exclusion of any other significant diversity. Examples of bicultural societies are found all over the world with different kinds of splits, including in:

Fijian Islands :      (54% indigenous, 38% Indo-Fijian)  
Rwanda: (85% Hutu, 15% Tutsi)
Northern Ireland: (45% Protestant, 40% Catholic)
Iraq: (62% Shi'a, 35% Sunni)
California: (44% Non-Hispanic white, 34% Hispanic)
Quebec: (81% Francophone, 9% Anglophone)
Tibet: (93% indigenous, 6% Han-Chinese)
Trinidad and Tobago: (40% Indian, 40% African)
Macedonia: (64% Macedonian, 25% Albanian)
Sudan: (52% black, 39% Arab)

For several of these places the following observations might come to mind:

(a) The most numerous group is not the top dog.
(b) The mandate of the government is shakey.
(c) They are not very safe places to visit.

There are some reasons to explain this, depending on the history of each region. A legacy of colonialisation has been the ascendency of minority groups to positions of power, who have managed to survive after whitey left by reinventing themselves. Some become technocrats and can rule on the strength of their skills and abilities. Others move into business. And some may just be plucky and ruthless enough to dominate through force. However if a privileged minority fails to use the right mix of stick and carrot on the majority, their rule may be turbulent and fleeting.

It is easier in multicultural societies for a minority to rule if it is the largest minority, but when the strength of the two largest groups are almost equal it is harder for one group to accept its own aquiescence to the other.