MANSOURA, Egypt — Elated that for the first time in their lives every ballot mattered, Egyptians flocked to the polls in record numbers on Saturday to vote in a referendum on a package of constitutional amendments that will shape the country’s political future after Hosni Mubarak’s overthrow.

From this provincial capital in the Nile Delta, across the sprawling capital of Cairo and beyond, voters were already waiting when the polls opened at 8 a.m., and the lines grew throughout the day, sometimes stretching until the wait exceeded three hours.

Gone was the heavy security presence of the Mubarak years, with only a few police officers and soldiers lingering around the crowded entrances but mostly standing apart from the proceedings.

“Before, I was not even allowed into the polling station,” said Mohamed el-Sayid Auf, a stooped 52-year-old engineer and Muslim Brotherhood supporter voting in a poor neighborhood here. “The police would tell me: ‘Go home. We already voted on your behalf. We know what is best for Egypt better than you.’