The Muslim Brotherhood, one of the Arab world's oldest Islamist movements and Egypt's largest opposition group, is well placed to play a prominent role as President Hosni Mubarak's rule teeters on the brink of collapse.
The movement is active in the protest movement massing in Cairo, Alexandria and other cities on Tuesday in an attempt to persuade Mubarak that after 30 years it is time to go.
But decades of severe repression have taught the Brotherhood to move cautiously, and the movement is anxious to preserve the impression that the protesters are part of a broad-based movement of which the Islamists are just one part.
Ironically, if the Brotherhood does emerge with unprecedented power, some of the credit will be Mubarak's.
Like many other Arab autocrats friendly with the United States and Europe, Mubarak has deliberately given the Islamist movement space, though on a tight leash, so that he could pose as the only plausible bastion against an Islamist government.
Although the government calls the Brotherhood a banned organisation, it has let the movement open offices, make statements and field candidates in parliamentary elections.
The US and European governments fell into the trap set by Mubarak and have refused to make contact directly with the
Brotherhood, for fear of angering the Egyptian government.
Distorted political environment
Foreign governments could not even argue that the Brotherhood was a "terrorist" organisation, because the movement renounced violence in the 1950s. Throughout Mubarak's presidency, it has struggled to take part in electoral politics.
A byproduct of Mubarak's strategy has been the ruthless elimination of all liberal democratic rivals who might appeal to foreign governments as alternatives to himself.
The most obvious example is Ghad Party founder Ayman Nour, who dared to stand against Mubarak in the country's first multicandidate presidential elections in 2005.
Nour, who won at least 8 percent of the vote and probably much more, spent the next few years in poor health in prison on what he says were fabricated charges of forging signatures.
In such a distorted political environment, where no free elections have taken place since at least 1952, it is impossible to judge the real popularity of the Brotherhood.
In the parliamentary elections of 2005, the first stages of which were relatively fair, it won 88 of the 165 seats it contested. In the latter stages police stopped people voting.
But, as the strongest opponent of Mubarak's National Democratic Party, the Brotherhood may have attracted many voters who did not share its Islamist agenda but wanted to register a protest against Mubarak and his party.
Another distorting factor is that most Egyptians refuse to vote at all, in the belief that the authorities usually make up the results. The real turnout is often less than 5 percent, so a well-organised group can sometimes make an impact.
Lay professional leadership
The popular uprising against Mubarak has sent shock waves across Israel and the United States, where the governments are worried that the Brotherhood might end up in power.
Israeli Prime Minister Benjamin Netanyahu said on Monday he feared Egypt could end up with a confrontational Islamic government such as the one which has ruled Iran since 1979.
The Muslim Brotherhood is certainly confrontational towards Israel and hence towards the United States. It has historic institutional links with the Palestinian Islamic movement Hamas and shares its belief in armed struggle against Israel.
But unlike the Shi'ite clerics who rule Iran, the Muslim Brotherhood has an overwhelmingly lay leadership of professionals with modern educations -- engineers, doctors, lawyers, academics and so on. The core membership is middle-class or lower middle-class.
Egypt in 2011 is also very different from Iran in 1979. Mubarak has allowed relative freedom of speech and access to information. Until last week there were no internet restrictions. Twelve million foreigners a year visit Egypt and foreign companies are deeply imbedded.
The Brotherhood has no equivalent to the Iranian doctrine of velayet-e faqih, or rule by the clerics. It advocates democratic pluralism, in the belief that, given time and the freedom to choose, Egyptians will opt for an Islamic state.
But rights activists fault the Brotherhood for insisting that the head of state must be a Muslim man, not a woman or someone from Egypt's Coptic Christian minority.
In recent years it has focused on political demands shared by most opposition groups, playing down a conservative social agenda which some Egyptians would find irksome.