ROME – Millions of pilgrims swamped the streets of Rome yesterday in what is developing into the greatest display of Christian fervor of modern times.

The phenomenal response to the death of Pope John Paul II both delighted and alarmed the Italian and Vatican authorities as they struggled to deal with an influx that threatened to overwhelm a modern European capital.

No one knew quite how many mourners were in the city. No one could predict how many were on their way. Some estimates put the eventual total at 5 million – twice as many as the normal population of the Eternal City.

Pilgrims were having to line up for at least 12 hours for a glimpse of the Holy Father lying in state in St. Peter’s Basilica on a bier near the crypt where he will be entombed tomorrow.

They did so cheerfully and without complaint, despite strong spring sunshine and a dearth of portable lavatories.

Occasionally, someone keeled over. The barriers channeling the crowds from side-street tributaries into the Via della Conciliazione leading into St. Peter’s Square would then be pulled back and the victim treated by the army of first-aiders and paramedics standing by.

Many of those waiting carried umbrellas to provide shade. Volunteers tossed bottled water into the queue in an attempt to ward off dehydration.

The Italian news agency ANSA reported that 1 million people had filed past the pope’s embalmed body by yesterday morning while a further million waited outside. The prefect of Rome, Achille Sera, admitted that contingency plans had not planned for the 4 million people he said had arrived in the city since Saturday.

Fabrizia Forghieri, 37, had been waiting for 10 hours with her 12-year-old daughter, Martina, before she reached the edge of St. Peter’s Square. “Of course it’s been worth it,” she said. “Something like this will never happen again.”

A few hundred yards – and several hours – back was Maria Church, who had arrived that morning from London with her son, Johnny, 11. “We just had to come,” she said.

The vast crowds displayed amazing self-discipline, but the volume of humanity was starting to rattle the organizers.

“People, this is a dramatic situation,” announced a security coordinator, Andrea Astolsi, over a loudspeaker. “This is a 14- to 15-hour wait.” Cell phone companies took to text messaging their customers with the news. But no one seemed deterred. As the day progressed, the crowds backed up so they blocked the bridges across the Tiber linking the Vatican to the rest of Rome and thronged the far bank.

Traffic was thrown into chaos as police closed off main roads. Every side street and square was choked with columns of pilgrims streaming toward the Holy See. Many were trendily dressed youngsters – the Papa boys and girls, as the Italian press has dubbed them. At Rome’s two airports, flights bearing more mourners landed every few minutes. The main Termini station was choked with passengers alighting from specially added trains.

Many had no idea where they would sleep. Every hotel room was booked.

A disaster expert drafted in to help with the operation, Gaetano Bastoni, said: “This is a unique event. The situation is evolving so quickly, it’s impossible to keep on top of it.”

Police closed the viewing line at 10 p.m. last night, turning back pilgrims in an effort to clear the basilica in time for tomorrow’s funeral, the Associated Press reported. Earlier, officials had used text messages sent by cell phones and electronic highway signs to try to curb the line of mourners, but those managing the crowd struggled to stop the sea of people.

Shops and businesses will shut and the city center will close to all traffic except emergency and police vehicles, and pilgrim shuttle buses.

The authorities have thrown up tent cities at the outskirts of the city and opened special hostels. They appealed to Romans to open their homes to the visitors. For tens of thousands, though, the only bed they were likely to find last night was a patch of pavement and, with luck, one of the blankets being distributed by the civil defense organization.

Airspace over Rome will be closed today and warships stationed off the coast 20 miles to the west to deter possible terrorist attacks at an event that will be attended by more than 200 world leaders. Thousands of special police officers have been ordered in. Despite the solemnity of the occasion, the pope’s obsequies are turning out to be a happy event.

There are few tears and little somber clothing on display. The waiting pilgrims whiled away the time chatting, singing hymns and folk songs, and watching television on giant screens. Pizza parlors along the route did a roaring trade, compensation at least for the large lines that formed to use their lavatories.

The Italian authorities have admitted that they seriously underestimated the numbers who would come to say goodbye to “John Paul The Great.”

If the funeral goes off without serious incident, it will largely be because of the self-restraint and good nature of the pilgrims. Last night, despite mass thirst, hunger, and fatigue, those qualities were still in evidence.