This is no longer an idle question. Even the United States, whose massive citadel-style embassy towers over the centre of Cairo, fears for Egypt's future. Anxious to avoid a repetition of the Iranian revolution - where their failure to form a relationship with the Islamic opposition turned an ally into an enemy when the Shah was dethroned - the Americans have been making discreet contact with the Muslim Brotherhood, whose calls for a nation governed by Sharia law are more moderate than those of the violent secret society el-Gamaat el- Islamiya (the Islamic Group).
According to members of el- Gamaat, however, the US embassy political section in Cairo attempted to establish contact with the organisation in 1991, only to have the communication broken off in June last year. El-Gamaat is trying to re-establish contact with the US through humanitarian affairs officials at the State Department in Washington, so far without apparent success.
Far more disturbing for President Mubarak's government, however, is the mounting evidence that el- Gamaat - far from being the Iranian- backed group that Mr Mubarak claims - has close relations with Saudi Arabia. For despite the impression conveyed by the US press and television networks after the World Trade Center bombing, Sheikh Omar Abdul-Rahman, the blind Egyptian prelate currently residing in New York, is not the head of the fundamentalist organisation.
The real leadership includes two Egyptians who fought as volunteers in the Afghan war - Mohamed Shawki el-Islambouly, the brother of the man who killed President Sadat, and Talaat Fuad Kassem - at least one of whom is now believed to be in Peshawar, in Pakistan. Both are said to owe loyalty to Abdul Rassoul Sayaf, a ferocious Afghan guerrilla fighter of the Wahhabi faith, the same sect as the Saudi royal family. One of the Egyptians charged with the World Trade Center bombing was also an Afghan veteran.
Much more to the point is that Mr Sayaf - like Mr Islambouly and Mr Kassem - received Saudi funding during the Afghan war; they are widely rumoured within el-Gamaat today to be still in receipt of Saudi cash. According to el-Gamaat sources, they received weapons and training during the Afghan war not from Iran but from the CIA. El-Gamaat's leadership in Pakistan has been sending direct warnings to the US embassy in Cairo and to the American University there, threatening US 'interests' in Egypt. Most of these warnings were sent by fax from a Peshawar telephone number.
While ruthlessly trying to suppress militant fundamentalism within their own borders, most Arab states have supported foreign Islamic radicals in order to weaken their rivals. The Saudis, for example, have also given substantial funding to the Islamic Salvation Front in Algeria - to the consternation of the Algerian government, whose public declarations against Islamic 'terrorism' are now being repeated almost word-for- word by the Interior Ministry in Egypt. The Egyptian authorities are well aware of the Saudi connection but dare not publicise their concern for fear of alienating their richest neighbour.
That the violent opposition to the Egyptian government is 'home- grown' is studiously ignored by the Cairo press but constantly discussed by Egyptians themselves. No conversation takes place without an argument about Islam's role in Egypt and the radicals' appeal to youth. Indeed, almost all el-Gamaat's recruits - save for Sheikh Omar - are young, in contrast to the elderly men who run all of the country's political parties and institutions. Egypt is not on the verge of revolution - the only civil war taking place is between el- Gamaat and the minority (and very frightened) Christian Coptic community - but it is in a frightening state of disequilibrium.
This is assisted by growing public anger, not only at the authorities' inability to crush el-Gamaat but by persistent reports that senior government officials, including a former defence minister, a prominent Egyptian newspaper executive and a former senior Egyptian intelligence officer, have been involved in corruption.
Earlier this month, the Prime Minister, Atef Sidki, announced that the Egyptian media were henceforth forbidden to report on a police investigation into the activities of a young Armenian woman named Lucy Artine, over whom three Egyptian officials are said to have resigned. Opposition newspapers in the capital have named the three officials as the former defence minister, retired Field Marshal Abdul-Halim Abu Gazzala, and two senior officials of the Interior Ministry, Police Major General Fadi el-Habashi and Major General Hilmi el-Fiqi.
President Mubarak has done his best to resist the pressure of the fundamentalists while encouraging the observance of Islam in what remains one of the least authoritarian nations in the Arab world. But the violent opposition to his rule is partly directed at the very relationship upon which it is based - Egypt's alliance with the US and, by extension, with Israel.
El-Gamaat wants to deprive Egypt of its income from foreign investment and tourism, forcing Mr Mubarak to make ever more desperate appeals for funds from Washington. That Egypt, Israel and the US now all see themselves as fighting the same Islamic enemies - with Israel helping to set the agenda for the battle against 'world terrorism' - merely provides further propaganda for the enemies of Mr Mubarak.
Not that el-Gamaat is without its internal divisions. Sheikh Omar has been in bitter dispute with another el- Gamaat prelate, Safwat Abdul Ghani. In an attempt to deprive the Sheikh of power, Mr Ghani announced that a true imam must possess all his senses, a deliberate attempt to disqualify the Sheikh through his blindness. The latter hit back by claiming that no imam could organise his people from captivity; for Mr Ghani is currently in an Egyptian prison after being captured by the police who - according to malicious rumour - were tipped off by Sheikh Omar's supporters.
Yet none of this can be of much comfort in Washington. As co-signatory of the Camp David agreement and guardian of the Suez Canal, Egypt is now more important to the US than the Shah of Iran ever was as 'policeman' of the Gulf. And if Egypt is to be radicalised amid the Islamic winds sweeping the Arab world, then Washington must somehow protect its relationship with Cairo. The Muslim Brotherhood may not be the ideal mechanism for this - but one of its first tasks should it ever acquire power would be the crushing of El- Gamaat.