With the current upheaval in Egypt, a quick look at the history of government there might help in considering what changes, if any, might be expected.
In the late 10th Century, the Fatimids conquered Egypt, transferring their capital there in 969. The Fatimids were an Arab family claiming descent from Mohammad’s daughter Fatima who established themselves among the Berber population in what is modern day Tunisia. They eventually established a Shia Caliphate across North Africa after defeating the Abbasid Caliphate.
Their power was based on foreign troops, particularly their Mamluk slave-soldiers. They eventually lost control of their various troops who began fighting each other, leaving their state vulnerable, first to the Crusades, and eventually to the leader of the army that defeated the Third Crusade.
In 1171 Saladin finally did away with the last Fatimid Caliph and declared himself ruler of Egypt. Saladin had been in Egypt fighting the Crusaders and simply took advantage of the chaos to create his own state.
Like the Fatimids, Saladin’s army was composed primarily of Mamluk slave-soldiers. When Saladin’s sons proved significantly less adept at both war and politics than Saladin, and the Crusaders returned, the Mamluks moved to replace the Ayyubids.
In 1259 Louis IX of France led the Seventh Crusade into Egypt. The reigning Ayubbid Sultan died suddenly and before his heir could arrive the Mamluks defeated the Crusaders and declared their own state in 1260.
The Mamluks were, as noted, slaves. They were typically Christians who were captured or purchased as children and converted to Islam. The Bahri dynasty was of Kipchak Turkic heritage, and managed to hold Egypt against both the Mongols and additional Crusades until a revolt that began in Syria spread through their realm and another Mamluk dynasty replaced them.
In 1377 the Bujri Mamluks, of Circassian heritage, took advantage of the latest chaos to replace the Bahri Mamluks. During their reign they fought against the Muslim ruler Tamerlane before eventually being conquered by the Ottomans and their Janissary slave-soldiers.
Although the Ottomans had overthrown the Mamluks they eventually turned most of the control of Egypt back to them, contenting themselves with appointing a Governor, and letting the wealthy Mamluk families who served as the nobility run things. Over time these families came to dominate politics so much as to be semi-autonomous, owing little more than token fealty to the Sultan.
In 1798 Napoleon carried out his plan to conquer Egypt in an attempt to cut off British trade to the Far East. Initially successful the combined British and Ottoman response, failing support from the Mamluk noble families, and decaying political situation in France caused Napoleon to leave the expedition, the remaining troops holding out until they negotiated a surrender to the British in 1802. Although of short duration the expedition opened the door for the next ruler of Egypt.
Muhammad Ali Dynasty
The Albanian leader of Ottoman troops sent to deal with the French, Muhammad Ali seized the opportunity to eliminate the last remnants of the Mamluks, expel the Ottoman governor, and declare himself ruler of Egypt. He fought for the Ottomans against the Sauds who were attempting to conquer the Hejaz (the area of Arabia containing Mecca and Medina), but later turned on them completely, seizing Syria, and threatening to overthrow the empire entirely. Intervention by the British and French, who did not want to see an expansion of Russian power if the Ottomans fell, forced him to settle, and he retained only Egypt. His children were nowhere near as competent as he was, and they swiftly fell under British control.
Starting in 1876 the British government began taking increasing control of the Egyptian government as it went bankrupt trying to conquer Sudan. This turned to complete occupation in 1882 when British troops landed. Under varying forms and names the British would control the government of Egypt through the descendents of Muhammad Ali until 1922.
Muhammad Ali Redux – Kingdom of Egypt
When the British finally gave up their protectorate the current ruler was declared a King. Despite the formal end of the protectorate Kings Fuad and Farouk were still considered puppets of the British, and discontent persisted throughout their reigns, exacerbated by the defeat in the 1948 Arab-Israeli War. In 1952 the Egyptian army mutinied, replacing Farouk with Fuad II, formally ending the monarchy in 1953.
Republic of Egypt
Following the overthrow of the monarchy, Egypt established a republic in 1953. Since then Egypt has had four Presidents. The first, Muhammad Naguib, was one of those idealistic rebels who actually expected to turn Egypt over to civilian rule. He lost a power struggle with Nasser and was forced out after holding office for a year. The other three, Gamal Abdel Nasser, Anwar El Sadat, and Hosni Mubarak, have all ruled effectively with the approval of the army, by way of the National Democratic Party, and under emergency law for most of the time since 1967. Despite the name it has always functionally been a military dictatorship, with more in common with the Mamluks than an actual republic.
Depending on how you view the Fatimid Caliphate, Egypt has been under military rule for 829 or all of the last thousand years.
Depending on how you view Soviet and American subsidies, Egypt has been under foreign influence or foreign dynasties for all or all but 58 of the last thousand years.
It seems almost certain that only direct foreign intervention will prevent the Egyptian military from determining who the next ruler of Egypt will be. All that remains uncertain is the exact identity of that person.