Islamists have already won a share of power in other countries in the wake of the Arab Spring uprisings and an election victory would be a symbolic shift in Algeria, which has one of the most rigidly secularist elites in the Arab world.
In the early 1990s, the military-backed elite overturned an election which Islamists were poised to win and then fought a conflict with them in which about 200,000 people were killed. Beyond the symbolism though, change will be limited.
The Islamists have close ties to the ruling elite, they are moderate, rarely mention religion, and parliament's restricted powers mean they cannot push radical reform even if they want to.
More hardline Islamists who do seek radical change, and who represent an influential and often volatile part of society, are outside the political process - some out of choice and some because they have been outlawed.
"The Islamists will very likely win, they will very likely form a coalition inside the parliament, they will make a lot of noise, but this will have very little impact on Algeria's political life," Mohamed Mouloudi, an editor and specialist on Islamic affairs, told Reuters.
Algeria has no reliable opinion polls but analysts and diplomats predict the six Islamist parties running in Thursday's election will pick up a bigger share of the vote than the traditionally dominant secularist parties.
The trend was evident on Saturday in the El-Harcha sports hall in the centre of the capital, Algiers.
Ahmed Ouyahia, the prime minister and leader of the secularist National Democratic Rally, gathered about 5,000 people for a rally but many seats were empty. A few hours later, the same venue was full for a rally held by the Islamist Front for Change.
While the Islamists who swept to power after the Arab Spring in Tunisia or Egypt were former dissidents who often spent years in jail for their beliefs, their counterparts in Algeria are more familiar with the inside of government limousines.
Most forecasts say the Green Alliance, a pact between three Islamist parties, will be the biggest contingent in the new parliament.
The Movement for Society and Peace (MSP), the biggest party in the alliance, was part of a pro-presidential coalition until last December, when its leader announced he was going into opposition.
It nevertheless kept several of its ministerial portfolios. One of those who stayed was Amar Ghoul, minister for public works. He heads the alliance's roster of candidates in the capital and is tipped by some as a possible prime minister.
A similar web of links exists between the ruling establishment and other Islamist parties even though they all say they are in opposition.
A former leader of El-Islah, another party in the Green Alliance, is now an advisor to President Abdelaziz Bouteflika.
At least one ex-senior member of Ennahda, the third alliance partner, has been given an ambassadorship. Abdelmadjid Benasra, head of the Front for Change, served as industry minister during Bouteflika's first term and used to be in the MSP.
Most of the Islamists in the election are also close to the ruling elite in terms of ideology. Their campaigns focus on bread-and-butter issues and make little mention of the role of Islam in public life.
In its speeches and campaign literature, the Green Alliance does not mention the integration of Sharia, or Islamic law, into the justice system. For many people in the Arab world, backing the adoption of Sharia is the test of a true Islamist.
At Amar Ghoul's campaign headquarters, a villa in an up-market street in Algiers, there was no sign last week of any religious symbols. The young woman at the reception desk was not wearing the Islamist head scarf.
Later the same day, Ghoul arrived in a convoy of cars and buses for a campaign stop in Oued Smar, an industrial suburb of the capital.
With a neat moustache and dressed in a polo shirt and suit jacket, he spent 45 minutes talking to customers in a cafe and then toured an apartment complex nearby. Religion was not discussed.
"People ask him about two things: jobs and housing," said a campaign aide.
For Hamdane Redouane, 44, this kind of pared-down Islamism is a sell-out. "The Islamists are no longer Islamists," he told Reuters. "All they want now is a small share of power, and they are even ready to implement a secular programme."
Redouane belongs to an important category of Algerian citizens - orthodox Islamists who have huge influence on a grass-roots level yet who do not have a political voice. They do not figure in next week's election.
Al Qaeda's north African wing, whose field commanders are Algerians, last month called on people to boycott the election and revolt against the elite. This group carries little sway in a society which is fed up with violence.
More influential are former members of the Front for Islamist Salvation, or FIS. This was the movement whose 1991 election win was cancelled by the military-backed government. Ex-leaders of the now-banned FIS, from exile, formed a new movement which was lobbying for a peaceful Arab Spring style revolt in Algeria.
This was curtailed when one of their leaders, a physicist called Mourad Dhina, was arrested in France in January after Algeria requested his extradition.
The Rachad movement, of which Dhina is a co-founder, said in a statement that he jailed to stop the true opposition to the military from exposing a corrupt electoral process. The most powerful group sitting out the election are Algeria's Salafists, followers of an ultra-purist interpretation of Islam. They control hundreds of mosques and have a vast network of charitable associations.
"Allah is the legislator, not man. This is why we do not recognize the parliament as a body in charge of producing laws," said Ahmed, a worshipper at a mosque in the Algiers suburb of Kouba, where the chief cleric is a spiritual leader of Algerian Salafism.
"We are not going to vote in the legislative election on May 10, and we urge our followers and friends to follow us," said Ahmed. "We believe that the laws are in the Koran."