The Arab spring marked the emergence of a new generation on the political scene and a definitive rupture with the dominant political culture of the past 60 years across the Middle East, especially in Egypt. However, the revolutionaries haven't taken power - they didn't want to.

Predictably, the Egyptian election brought the triumph of Islamist parties. With deep roots in society, enjoying a legitimacy conferred by decades of political opposition, and defending conservative and religious values shared by a majority of the population, the Muslim Brotherhood was able to attract votes well beyond an ideological hard core because it looked like a credible party of government. More surprising was the strong showing of the Salafist al-Nour Party. Even allowing for the rise of Salafism in Egypt, it is hard to see what was motivating those who voted in such numbers for al-Nour. Was this a protest vote, or a vote for sharia law? Only time will tell.

Nevertheless, whatever happens, the victory of the Islamists raises doubts about whether the process of democratisation in Egypt and elsewhere will continue. And for many in the west, the Arab "winter" has reaffirmed their conviction that Islam is incompatible with democracy.

Thus, it seems there are two entirely con­tradictory images of Arab society: on the one hand, the youth of the Arab spring, eager for freedom and democracy, individualist, tolerant and liberal, but inexperienced and in the minority; on the other hand, the Islamist electorate, conservative, traditionalist and anxious about the risk of disorder.

It would be a mistake, however, to think of these as two clearly defined camps in conflict with one another (which is the picture that the French media tend to paint of Tunisia, for instance). In fact, Arab societies are as complex as any other. The truth is that we are in the middle of a long-term process, in which changes in Arab society and the evolution of religion - what I and others have called "post-Islamism" - struggle to find expression in a political arena still dominated by actors from the old world. Just as the Tea Party in the United States is a reaction to the election of Barack Obama that remains incomprehensible so long as one doesn't take into account the growth of ethnic minorities and the retreat of traditional values among the younger generations, so the conservative wave in Arab countries should be understood in the light of social and cultural changes that are both irreversible and highly destabilising.

To grasp what is happening, we must set aside a number of deep-rooted prejudices. The first of these is the assumption that democracy presupposes secularisation. The second is the idea that a democrat is, by definition, also a liberal. Historically, this has not been the case. The American Founding Fathers were not secularists; for them, the separation of church and state was a way of protecting religion from government, not the reverse. The French Third Republic was established in 1871 by a predo­minantly conservative, Catholic, monarchist parliament that had just crushed the Paris Commune. Christian democracy developed in Europe not because the church wanted to promote secular values, but because it was the only way that it could maintain political influence. Finally, let's not forget that populist movements in Europe today align themselves with Christian democracy in calling for the continent's Christian identity to be inscribed in the EU constitution.

Islamists in the Arab world deplore secularisation, the influence of western values and the excesses of individualism. Everywhere, they seek to affirm the centrality of religion to national identity and they are conservative in all areas except the economy. And in Egypt, like any party swept to power in an electoral landslide, they are tempted to think that they can dispense with the grubby business of forming alliances and distributing government posts equitably. In any case, why would the Islamists, with no democratic culture to speak of, behave like good democrats who believe in pluralism? No doubt many activists are asking themselves the same question.

The Islamists are certainly neither secularists nor liberals, but they can be democrats. It is not the convictions of political actors that shape their policies but the constraints to which they are subject. The Islamists are entering an entirely new political space: this was not a revolution in which a dictatorship was replaced by a regime that resembled its predecessor. There have been elections and there will be a parliament. Political parties have been formed and, whatever the disappointments and fears of the secular left, it will be difficult simply to close down this new space, because what brought it into being in the first place - a savvy, connected young generation, a spirit of protest - is still there. Islamist movements throughout the region are constrained to operate in a democratic arena that they didn't create and which has legitimacy in the eyes of the people.

It is significant, in this regard, that nowhere has the cult of the charismatic strong man reappeared. Instead, there are political parties and a new culture of debate that has influenced even the Islamists. These developments were not created by accident but are the direct consequence of deep social transformations that are irreversible, whatever the strength of the reactions to them. After all, you can't change a society by decree. In Iran, all the indicators suggest that society has become more modern and secular under the mullahs; although the law allows girls as young as nine to be married, statistics show that the average age at which Iranian women get married has continued to rise - today it stands at more than 25. In short, we are not seeing a return to a traditional society.

Furthermore, the protest movements in Egypt and Tunisia were shaped not by an ideology as all-encompassing as the regimes that they toppled (which was the case in Iran in 1979), but by the ideals of democracy, pluralism and good governance. In Iran in 1979, elections were held in the name of the Islamic Republic. The message was clear: this was an ideological revolution (even if there was disagreement about its complexion between the red of the Marxist-Leninists and the green of the Islamists). There is nothing of the kind in either Egypt or Tunisia. There is no revolutionary or ideological dynamic.

The "Islamic" electorate in Egypt today is not revolutionary; it is conservative. It wants order. It wants leaders who will kick-start the economy and affirm conventional religious values, but it is not ready for the great adventure of a caliphate or an Islamic republic. And the Muslim Brotherhood knows this. It needs to attract voters because it doesn't have the means to seize power by force, which in any case it does not wish to do. And even if it did, it does not have the technical wherewithal to do so, as it doesn't control the police or the armed forces and has no paramilitary militia.

Moreover, the Islamists don't enjoy a religious monopoly of the public sphere. There are other movements, such as the Sufis and the Salafists. The paradox of the Arab spring is that al-Azhar Mosque in Cairo, one of Egypt's most important religious institutions, has found a new legitimacy: the imam of al-Azhar, Sheikh Ahmed el-Tayeb, has become an advocate of human rights, liberty and, above all, the separation of religious institutions from the state. This means that, in contrast to Iran, the Muslim Brotherhood is unable to "say what Islam says". The religious arena, too, has become pluralistic and open to democratic pressure, even if, for the faithful, there are some things that remain non-negotiable.

That said, there is no agreement over what is and is not negotiable beyond the centrality of Islam. Should there be a body that determines the Islamic-ness of laws? If there should, who ought to be nominated to it and by whom? Should the hudud or corporal punishment be applied in cases where religious laws have been violated? Is conversion to Christianity possible for a Muslim?

It is on the question of the definition of religious liberty that we can expect the most vigorous debates. If the Muslim Brotherhood presents itself as the protector of the rights of the minority Coptic Christians in Egypt to practise their religion, is it ready to make religious freedom an individual human right (abandoning the concept of apostasy in the process), rather than the collective right of a minority?

The debate has already started. Abdel Moneim Abul-Fotouh, a Muslim Brotherhood dissident, declared in May last year: "Nobody should interfere if a Christian decides to convert to Islam or a Muslim decides to leave Islam and become a Christian."

Whenever the implementation of Islamic religious norms comes up for discussion, there is an internal debate in the institutions concerned. The result is that one cannot simply oppose the "religious" bloc with the "secular" one. Democratisation has affected the community of believers, too.

The Salafists will certainly try to raise the stakes over sharia law and to make the Muslim Brotherhood face up to the contradictions of its position. But they have also leapt into the political realm, forming parties while contesting the very idea of political parties in the name of Islam. In their case, this is the compliment that vice pays to virtue: they know that without a parliamentary presence they would lose their influence.

All the same, the Salafists are anything but a party of government; they have no programme beyond the introduction of sharia, and the most realistic among them (including some in al-Nour) are perfectly aware of this. The Muslim Brotherhood and the Salafists are fated to be rivals, and so one cannot rule out the possibility of them entering into unexpected alliances with other political forces.

There is one further set of constraints on both the Islamists and the Salafists, and these are geostrategic. Neither was elected on a programme of jihad or support for the Palestinians. The Arab spring and Arab winter did not turn on international questions, whereas the Nasser­ite and Ba'athist revolutions, Anwar al-Sadat's counter-revolution of 1974 (when he opened up Egypt's economy and swapped the Soviet for the American embrace) and the Islamic revolution in Iran were all defined by the international conflicts of their time. Foreign affairs were absent from the electoral campaigns this past year of both the Muslim Brotherhood and the Salafists. Certainly the Israeli-Palestinian conflict remains important on an emotional level, but no one is ready to endanger stability and economic development for jihad.

The Islamists don't like Israel, and in this respect they are in step with Arab public opinion, but they are not willing to go to war. They have accepted the existing geostrategic constraints. The Tunisian invitation to Hamas (which follows the one extended to the Palestine Liberation Organisation after the Israelis took Beirut in 1982) is evidence of continuity rather than rupture. The care that the Muslim Brotherhood has taken to open a dialogue with western diplomats is another sign that it is accepting strategic realities. There is no alternative, especially not of an opening towards Iran. The Saudis and the Qataris have played a significant offstage role here, the former in pushing the Salafists to run for election, the latter in supporting the Muslim Brotherhood wherever it stood.

The major conflict that is taking shape is not a clash between the Muslim world and the west. Rather, it is the one that pits the conservative Sunni Arab world against the "Shia crescent" around Iran, with Saudi Arabia's "unholy alliance" with Israel in the background. The Brotherhood will struggle to carve out a distinct role for themselves in this context, and they know it. In the final analysis, the victory of the Islamists is part of the normalisation of the Arab world, as much in internal affairs as on a geostrategic level.

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