Story highlights

NEW: Several hurt in fresh Tahrir Square clashes

Report: Egypt's stock market sees an unprecedented wave of buying

Voters pick members of the lower house of Parliament

The lower house will be tasked with drafting Egypt's new constitution

Cairo CNN  — 

Reveling in their opportunity to vote in a post-Hosni Mubarak era, Egyptians headed to the polls Tuesday for the second day of the country’s parliamentary elections.

The voting this week marks the first time some Egyptians – young and old – have ever cast ballots. Citizens are picking members of the lower house of Parliament, which will be tasked with drafting a new constitution.

Egypt’s stock exchange opened considerably higher Tuesday and saw an unprecedented wave of buying amid the elections. But there were more street clashes after nightfall in Tahrir Square, the epicenter of recent protests against the military council that took power after Mubarak’s ouster.

At least a dozen gunshots rang out and several people were injured near the Egyptian Museum, at the entrance to the plaza. Ambulances darted in and out of the square late Tuesday as the fighting continued.

The melee began with fights between vendors and protesters who began throwing rocks and attacking their kiosks with sticks. The protesters complained some vendors were giving demonstrations a bad image by selling marijuana, said Mina Hagras, one of the demonstrators who has been camped in the square.

“This is not the spirit of the revolutionaries or the square,” Hagras said. “They warned them. They did not stop. So they took matters in their own hands and beat them up. Now, state TV is saying all the protesters in square are thugs and drug users. This is not fair.”

The state-run Middle East News Agency, citing a military source, said there were no police or troops in the square at the time.

Tuesday’s balloting came after logistical problems and illegal campaigning marred the first day of balloting on Monday. Voters decried the late opening of polling stations and a delay in the arrival of ballots, leading the head of Egypt’s election committee to promise a smoother voting process Tuesday.

Election officials said they have received 964 complaints, 579 of which have been addressed, according to Egypt TV. State TV reported that 25 people were injured in election-related violence.

Activist Hafez Abu Saeeda, of the Egyptian Organization for Human Rights, said on Twitter he was in Al-Khaleefa “working on an election tour, and an attack took place on our supporters before I arrived.” The army was able to control the situation immediately, he said. One person was injured.

But many voters expressed jubilation at their chance to help build a new Egypt after a popular revolt toppled President Mubarak’s 30-year regime in February.

“Before, there was always cheating. Now – I could be wrong – but I think my vote will count,” Mohamed Rida’a Mohamed Abdulla said as he left a Cairo polling station.

Some polling areas were segregated by gender. Lines at both men’s and women’s stations snaked around buildings for hours.

“It’s an awakening,” one woman said, beaming, at a Cairo polling station. “I’m very happy, and I feel that even when I see old ladies hardly walking, it makes me feel that really Egypt is reviving.”

The stakes are high for Egyptian women, who worry that if Islamists gain a majority in the lower house of Parliament, their hopes for a more liberal life will be quashed.

In Alexandria, the Al Noor Salafi Muslim party and the Freedom and Justice Party accused one another of breaking an “honorable agreement” aimed at cooperation. The Freedom and Justice Party is part of the once-banned Muslim Brotherhood, one of the nation’s largest organizations.

Yousri Hamad, a spokesman for the Al Noor Salafi party, said the Muslim Brotherhood spread false rumors and launched a “smear campaign” against the party.

“We were not as prepared for the elections as we should have been and did not spend enough money on the campaigning,” Hamad said.

But Essam Erian, spokesman for the Freedom and Justice Party, said the Salafis had breached the agreement by making such accusations without evidence.

Ali Al Dali, an official monitor for the Egyptian Association of Human Rights, said eight cases of vote-buying had been documented in Alexandria, and police had been notified. About 45% of eligible voters in the city had cast ballots, he said.

Elections for the lower house are scheduled to take place in three stages, based on geography. The last of the three stages is set to take place in January.

Upper house elections will run between January and March.

Presidential elections will be held by June, according to the Supreme Council of the Armed Forces, Egypt’s acting ruling body. Military leaders have said they will hand over power to a new government when one is elected, but many Egyptians say they don’t trust the council and fear the military will cling to power.

Over the past two weeks, at least 42 people have been killed in clashes as protesters called for an immediate end to military rule. An additional 3,250 have been wounded, according to the Health Ministry.

Some Egyptians expressed skepticism or even boycotted the voting on Monday.

“There is no inclination that the judiciary is independent, so there is no way to prove the election will be free and fair,” said Amr Hamzawy, a 32-year-old shopkeeper.

Despite the masses who flocked to polling stations Monday, some remained cautious about how much Egypt could evolve after one election cycle.

“We’re not changing in one month, or a year, or five years. It will take a long time to change from one system to the other,” one woman said on the streets of Cairo. “We’ve been going with this system for the past 30 years, and it’s not like a button we push to change everything.”

CNN’s Ivan Watson, Leone Lakhani and Jim Clancy and journalists Mohamed Fadel Fahmy and Ian Lee contributed to this report.