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A coregency (or co-principality) is the situation where a monarchical position (such as king, queen, emperor or empress), normally held by only a single person, is held by two or more.
Historical examples 
Historical examples of this include the coregency of Frederick I of Austria and Louis the Bavarian over the Kingdom of Germany, and the coregency of William and Mary over England (along with Wales), Scotland, and Ireland. It was also found in Sparta with two Kings, San Marino with two Captains Regent, the ancient Roman Empire (by determination of Hadrian) and the Byzantine Empire, Ancient Egypt and Nubia, in these cases as a balance between King and Queen, male and female. Jure uxoris Kings in Kingdoms such as Spain and Portugal can also be found (Ferdinand V and Isabella I of Castile, Philip I and Joanna of Castile, Peter III and Maria I of Portugal, etc.).
City of Maastricht 
The city of Maastricht was under the joint jurisdiction (parage) of the duke of Brabant and the prince-bishop of Liège. In 1648 it became a real condominium of two independent states, the Principality of Liège and the republic of the United Provinces. The coregency of the last was no longer held by a person but by the Estates-General of the Netherlands (until 1794).
Ancient Egypt 
Another example is in Ancient Egypt, mainly in the Middle Kingdom, the Pharaoh occasionally appointed his successor (often one of his sons) as coregent, or joint King, to ensure a smooth succession. The Pharaoh also did this when he was elderly or unable to rule his country on his own (such as the case of Thutmose III and Amenhotep II or Amenemhat I and Senusret I). The existence of the practice makes establishing firm dates in Egyptian chronology more of a challenge, as the lengths of coregencies are often uncertain and complicate the use of accepted regnal lengths to establish dates. Some of the Queens of Egypt rose to a status of equal to the God-Kings, becoming co-rulers and / or at least as important in religious affairs, and were even portrayed with the same size as their male consort and even with the same size as the other Gods of Egypt. Such were the cases of Hatshepsut, Nefertiti, Nefertari and the Nubian Egyptian Queens. In the Ptolemaic Dynasty women finally rose to become equal co-rulers with men and even challenging them in order to become their respective consorts. This was due to a progressive improvement of the already high status of women in the Egyptian society, as well as to the religious principle of balance (Maat) between male and female. In Nubia, Queens like Amanishakheto and Amanitore were crowned alongside Kings at Dangeil and had both their pyramids at Meroë with the same height and side by side, and exerced power at the same level, even commanding armies. In Ethiopia, Kandakes also reached and hold this or a similar status.
Date discrepancies 
In the book The Mysterious Numbers of the Hebrew Kings, Edwin R. Thiele proposed coregency as a possible explanation for discrepancies in the dates given in the Hebrew Bible for the reigns of the kings of Israel and Judah. At least one coregency is explicitly documented in the Bible: the coronation of King Solomon occurred before the death of his father David. Some Kings of Egypt, specially during the Twelfth Dynasty, also practised this custom, by associating their own sons in order to both prepare them for the office and prevent anyone else from usurping the throne, especially during its earlier days.