In Europe, the popular uprisings in North Africa and the Middle East have been interpreted using a model that is more than 30 years old: the 1979 Islamic revolution in Iran. Commentators have been expecting to see Islamist groups - the Muslim Brotherhood and their local equivalents - either at the head of the movement or lying in wait, ready to seize power. But the discretion of the Muslim Brotherhood has surprised and disconcerted them: where have the Islamists gone?

Look at those involved in the uprisings, and it is clear that we are dealing with a post-Islamist generation. For them, the great revolutionary movements of the 1970s and 1980s are ancient history, their parents' affair. The members of this young generation aren't interested in ideology: their slogans are pragmatic and concrete - "Erhal!" or "Go now!". Unlike their predecessors in Algeria in the 1980s, they make no appeal to Islam; rather, they are rejecting corrupt dictatorships and calling for democracy. This is not to say that the demonstrators are secular; but they are operating in a secular political space, and they do not see in Islam an ideology capable of creating a better world.

The same goes for other ideologies: they are nationalist (look at all the flag-waving) without advocating nationalism. Particularly striking is the abandonment of conspiracy theories. The United States and Israel - or France, in the case of Tunisia - are no longer identified as the cause of all the misery in the Arab world. The slogans of pan-Arabism have been largely absent, too, even if the copycat effect that brought Egyptians and Yemenis into the streets following the events in Tunis shows that the "Arab world" is a political reality.

This generation is pluralist, undoubtedly because it is also individualist. Sociological studies show that it is better educated than previous generations, better informed, often with access to modern means of communication that allow individuals to connect with one another without the mediation of political parties - which in any case are banned. These young people know that Islamist regimes have become dictatorships; neither Iran nor Saudi Arabia holds any fascination for them. Indeed, those who have been demonstrating in Egypt are the same kinds of people as those who poured on to the streets to oppose Mahmoud Ahmadinejad in 2009. (For propaganda reasons, the regime in Tehran has declared its support for the opposition movement in Egypt, though this is little more than a settling of scores with Hosni Mubarak.) Many of them are religious believers, but they keep their faith separate from their political demands. In this sense, the movement is "secular". Religious observance has been individualised.

Above all, people have been dem­onstrating for dignity and "respect", a watchword that emerged in Algeria in the late 1990s. And the values to which they are laying claim are universal. But the "democracy" that is being called for is not foreign, and therein lies the difference from the Bush administration's attempt to promote democracy in Iraq in 2003. That did not work, because it lacked political legitimacy and was associated with a military intervention. Today, paradoxically, it is the waning of US influence in the Middle East, together with the pragmatism of the Obama administration, that has allowed a native and fully legitimate demand for democracy to be expressed.

That said, a revolt is not a revolution. The new popular movement has no leaders, no structure and no political parties, which will make the task of anchoring democracy in these former dictatorships difficult. It is unlikely that the collapse of the old regimes will automatically lead to the establishment in their place of liberal democracies, as Washington once hoped would happen in Iraq.

What of the Islamists, those who see in Islam a political ideology capable of solving all of society's problems? They have not disappeared, but they have changed. The most radical of them have left to wage international jihad; they are in the desert with al-Qaeda in the Islamic Maghreb, in Pakistan or the suburbs of London. They have no social or political base. Indeed, global jihad is completely detached from social movements and national struggles. Al-Qaeda tries to present itself as the vanguard of the global Muslim "umma" in its battle against western oppression, but without success. Al-Qaeda recruits deracinated young jihadists who have cut themselves off entirely from their families and communities. It remains stuck in the logic of the "propaganda of the deed" and has never bothered to try to build political structures inside Muslim societies.

Because al-Qaeda tends to concentrate its activities in the west or aims at so-called western targets elsewhere, its actual impact is next to nil.

It is a mistake, therefore, to link the re-Islam­isation that has taken place in the Arab world over the past 30 years with political radicalism. If Arab societies are more visibly Islamic than they were 30 or 40 years ago, what explains the absence of Islamic slogans from the current demonstrations? The paradox of Islamisation is that it has largely depoliticised Islam. Social and cultural re-Islamisation - the wearing of the hijab and niqab, an increase in the number of mosques, the proliferation of preachers and Muslim television channels - has happened without the intervention of militant Islamists and has in fact opened up a "religious market", over which no one enjoys a monopoly. In short, the Islamists have lost the stranglehold on religious expression in the public sphere that they enjoyed in the 1980s.

Dictatorships in the Arab world, though not in Tunisia, have often favoured a conservative Islam that is highly visible but not especially political, and that is obsessed with controlling public morals. (The wearing of the hijab, for instance, has become commonplace.) This has meshed with the "Salafist" movement, which emphasises the re-Islamisation of individuals rather than the development of social movements. What has been perceived in the west as a great, green wave of re-Islamisation is in fact nothing but a trivialisation of Islam: everything has become Islamic, from fast food to women's fashion. The forms and structures of piety, however, have become individualised, so now one constructs one's own faith, seeking out the preacher who speaks of self-realisation, such as the Egyptian Amr Khaled, and abandoning all interest in the utopia of an Islamic state. The Salafists concentrate on the preservation of religious values and have no political programme. Moreover, other religious currents until now regarded as being in decline, such as Sufism, are flourishing once more. This growing diversity of faith goes even beyond the confines of Islam, as in the cases of Algeria and Iran, where there has been a wave of conversions to Christianity.

It is also a mistake to see the dictatorships as defending secularism against religious fanaticism. With the exception of Tunisia, authoritarian regimes in the Arab world have not made their societies secular; on the contrary, they have reached an accommodation with a neofundamentalist form of re-Islamisation in which the imposition of sharia law is called for without any discussion of the nature of political power. Everywhere, official Muslim institutions, based on an austere conservative theology, have been co-opted by the state. This has become so effective that the traditional clerics trained at al-Azhar University in Cairo no longer have anything to say about the main social and political questions of the day. They have nothing to offer a younger generation looking for ways of living their faith in a more open world.

These developments have also affected Islamist political movements, as is exemplified by the changing face of the Muslim Brotherhood in Egypt and al-Nahda, the "renaissance party", in Tunisia. The Muslim Brotherhood has changed in response to troubling events, as much in what seemed like success (the Islamic Revolution in Iran) as in defeat (the repression that has been meted out to it everywhere). A new generation of militants has drawn lessons from this, as have such veterans as Rachid Ghannouchi, founder of al-Nahda. They have understood that seeking to take power in the wake of a revolution leads either to civil war or to dictatorship. And in their struggle against repression, they have come into contact with other political forces and formations. Knowing their own societies well, they are aware that ideology carries little weight within them. They have also learned lessons from Turkey, where Recep Tayyip Erdogan and the AK party have succeeded in reconciling democracy, electoral success, economic development and national independence with the promotion of values that are, if not Islamic, at least "authentic".

Above all, the Muslim Brotherhood no longer advocates an alternative economic and social model. The Brothers have become conservative with regard to morality and liberal on the economy. This is without doubt the most striking evolution in their outlook, because, in the 1980s, Islamists claimed to defend the interests of the oppressed classes and called for state ownership of the economy and redistribution of wealth. Today, the Muslim Brotherhood in Egypt endorses Mubarak's agricultural counter-reforms, which have returned to landowners the right to raise prices and sack tenant farmers. So complete has this transformation been that Islamists are now wholly absent from the social movements active in the Nile Delta, where there has been a resurgence of the "left", particularly of trade union militancy.

However, the embourgeoisement of the Islamists is at the same time an asset for democracy, because it pushes them towards reconciliation and compromise, and into alliances with other political forces. It is no longer a question, therefore, of attempting to establish whether or not dictatorships are the most effective bulwark against Islamism; Islamists have become players in the democratic game. Naturally, they will try to exert control over public morality, but, lacking the kind of repressive apparatus that exists in Iran, or a religious police on the Saudi model, they will have to reckon with a demand for liberty that doesn't stop with the right to elect a parliament. In short, the Islamists will either identify themselves with the conventional, Salafist tradition, abandoning in the process any pretence to reconceive Islam's place in modernity, or else they will make an effort to rethink their understanding of the relationship between religion and politics.

In Egypt, the Muslim Brotherhood will play a central role in the coming changes as long as the revolt remains largely apolitical. For the moment, this is still the politics of protest; it is not the dawn of a new type of regime. Moreover, Arab societies remain somewhat conservative. The middle classes that developed following the period of economic liberalisation want political stability. They are protesting, above all, against the predatory nature of dictatorship. Here, a comparison between Tunisia and Egypt is illuminating. In Tunisia, the extended Ben Ali clan weakened all its potential allies by refusing to share not only power, but wealth, too. The business class was swindled by the ruling family and the army marginalised both politically and financially. The Tunisian army was poor, and thus had a corporate interest in seeing the advent of a democratic regime that would give it a bigger budget.

In Egypt, by contrast, the regime has had a much larger social base, and the army was involved not just in shoring up political power but also in the administration of the economy, with all the benefits that flowed from that. In this respect, that country is typical of the Arab world. Democratic movements throughout the region will therefore come up against deeply rooted networks of clientelism. Is the demand for democracy capable of overcoming complex arrangements of allegiance and belonging, in the army, among tribes and among the political elite? To what extent will regimes be able to exploit old allegiances - among the Bedouins in Jordan, say, or the tribes of Yemen? Conversely, can such groups themselves become actors in the movement for democratic change? And how will religion adapt to the new situation?

The process of change will undoubtedly be long and chaotic, but one thing is certain: the age of Arab-Muslim exceptionalism is over. Recent events point to profound transformations in Arab societies which have been under way for some time, but which until now have been obscured by the distorting optic of western attitudes towards the Middle East. What the convulsions in Egypt and Tunisia show is that people in those countries have drawn the lessons of their own history. We have not finished with Islam, that is for sure, nor is liberal democracy the "end of history", but we must at least learn to think of Islam in relation to an "Arabic-Muslim" culture that today is no longer closed in on itself - if it ever was.

Olivier Roy is professor of social and political theory at the European University Institute in Florence. His most recent book is "Holy Ignorance: When Religion and Culture Part Ways" (C Hurst & Co, £20)

This essay, written exclusively for the New Statesman, was translated from the French by Jonathan Derbyshire