CAIRO—Egyptians went to the polls on Wednesday to vote in the second of three rounds of parliamentary polls that analysts say will determine whether members of the ex-regime will keep a toehold in the nation's postrevolutionary legislature.

Voters largely rejected the remnants of former President Hosni Mubarak's government in the first round of voting that began late last month, handing them at most a handful of seats.

But it is the second round that will gauge whether Egypt's revolution has firmly convinced voters to reject the autocratic, secular-minded leadership whom protesters ousted last winter. The two-day polls that began Wednesday will bring out voters in more tradition-minded rural areas where prominent local members of the former regime held sway over large clans—including Monoufiya, the hometown of Mr. Mubarak, who is now on trial for murder.

The dwindling power of Egypt's former regime remnants or "feloul" as they are known in Arabic, could open the curtain on a new act in Egypt's revolution. With parliamentary elections now in full swing, the axis of debate in Egyptian electoral politics may have finally shifted from regime vs. opposition, to Islamist vs. secular.

Regional Upheaval

"There was this fear that the future assembly would be dominated on the one hand by the Muslim Brothers and on the other by supporters of the National Democratic Party," said Mustafa Kamal Al Sayyed, a political-science professor at the American University in Cairo, referring to Mr. Mubarak's dissolved party, the NDP. "The concern with the feloul is outdated now."

High turnout and few irregularities were reported during the first day of the second round of voting. The polls, which opened Wednesday in nine of Egypt's 27 governorates, will remain open Thursday. The third voting round ends in January.

Analysts and voters said they expected Islamist political parties, led by the Muslim Brotherhood's Freedom and Justice Party and the ultraconservative Nour Party, to dominate as they did in last month's first polling.

Anxiety over the feloul nearly derailed Egypt's first postrevolutionary parliamentary elections. Last fall, the powerful Muslim Brotherhood threatened to boycott the vote if the feloul weren't prohibited from running.

The Brotherhood conceded when the country's interim military leadership altered the electoral system, limiting unaffiliated party candidates—among which the feloul were expected to thrive—to only one-third of the 498 parliamentary seats.

A second measure to limit the feloul's influence occurred when the military passed a watered-down version of a "Treachery Law" in a concession to protesters last month. The law forbids politicians who have been convicted of fraud or vote-rigging from running for parliament.

Some analysts had expected the feloul to win nearly as many seats as the Islamists, who have so far won more than a combined 60% of the vote.

That now seems unlikely. If the trend of rejecting the feloul continues into the second round, it could temper anxiety that a lingering former regime will pollute Egypt's new parliamentary system with corruption, nepotism and clientalism.

On the other hand, a shift away from the old order could unsettle old family rivalries and sectarian tensions that simmer just below the calm surface of impoverished Upper Egyptian cities like Sohag.

In Sohag, feloul candidates are more than members of the former regime: They are scions of family systems whose roots reach beyond the Mubarak regime to an agrarian past in which a landed gentry exercised sole political power, meted out favors and punishment, and kept the peace among clans.

"Over here, the most dominant factor in the elections is the family and tribal factors rather than political ideologies and the relations between individuals," said Hazem Hammadi, a NDP member who has represented Sohag in Parliament since 2000 and is again a candidate.

Mr. Hammadi was seated in the dusty elegance of his campaign headquarters below a large black-and-white picture of his great-grandfather shaking hands with King Farouq, the British-backed monarch whom the Egyptian military ousted in a 1952 coup. Mr. Hammadi's relatives, who are helping his campaign, said the Hammadi clan alone claims up to 5,000 members.

Islamist politicians and the newly minted liberal candidates don't know the first thing about satisfying the competing clan interests that define Sohag's local politics, Mr. Hammadi said. "I don't think the Freedom and Justice Party can protect this city," he added.

Indeed, violence between Christians and Egypt's Muslim majority regularly break out in cities such as Sohag, as do score-settling fights between sprawling clans. Most recently, at least three people died and a police station was torched in August during violence between rival villages. Even those who have campaigned against the feloul acknowledge that some places are better left to their traditions.

"The faloul in Upper Egypt are not the businessmen who have corrupted Egypt," said Mamdouh Hamza, a prominent pro-democracy activist.

Mr. Hamza's secular-minded "National Council" of intellectuals helped launch the "Catch the Feloul" website that identified former regime members and spread their names to voters via social-networking services to raise awareness among voters. But he was resigned to the endurance of the regime remnants in Upper Egypt.

"They are large families, large tribes and their chiefs and important people who must have a seat in parliament," he said. "This is how it goes."

Despite Mr. Hammadi's confidence that the old, violent order will once again carry him to parliament, few voters in the impoverished Nasser City district of Sohag appeared to count themselves among his supporters.

"The only problem with Sohag is revenge and vengeance," said Yasser Mohammed, the owner of a popular coffee shop within sight of a nearby polling station. "But a lot of people are better at those situations" than Mr. Hammadi, he said.

Many voters in the neighborhood said that rather than calming angry clans, Mr. Hammadi incited them, playing their passions off each other to consolidate his control. Few could point to one thing Mr. Hammadi has done to benefit Sohag and fewer still had reported ever having met him.

Mr. Mohammed's friend, Yusuf Ali, described Mr. Hammadi as "a criminal" who earned a reputation for extracting confessions via torture while he was an officer in the state security services in the 1990s.

Mr. Hammadi denied having used torture, despite that a 2006 report from the Cairo-based Nadim Center for the Rehabilitation of Violence Victims cited witness testimony to corroborate such reports.

"Like most of the dissolved NDP, no one is going to vote for him," said Mr. Ali. "He's going to fall and it's going to be an ugly fall."