The off-the-field calm of the World Cup's opening day extended into Saturday, which featured an English team backed by tens of thousands of often-rowdy fans.

English police believe they've corralled the main potential troublemakers by ordering more than 3,500 known soccer hooligans to fork over their passports. But with up to 65,000 English watching their team beat Paraguay 1-0 — one of three games in different cities on the tournament's second day — security was heavy.

Frankfurt police were ready wherever fans congregated, some wearing helmets and bulletproof vests also toted video cameras.

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Flocks of exuberant English supporters prepared for the game by heading for the bar in the morning. By the final whistle, afternoon heat and the victory persuaded many to plunge into the River Main, which bisects this financial capital and is home to a giant, floating screen for public viewing.

Police reported arresting 20 people overnight, mostly for alcohol-related offenses, but there were no reports of post-game scuffles or new arrests during the day.

"They all seem to be happy," said police spokeswoman Gabi Goebel of the estimated 65,000 English fans in town — 40,000 at the stadium and 25,000 around the city center.

One Englishman believes his country's fans have changed since violent eruptions such as at the last World Cup held in Europe, the 1998 tournament in France.

"The people here, I think, have realized that England's fans are not what they have been portrayed to be," said Luke Walters, who watched the game with friends at a Frankfurt restaurant.

There were no reports of trouble at the day's second game, between Sweden and Trinidad and Tobago.

That didn't mean everyone was docile.

On Friday night in Frankfurt, "there was a fairly tense atmosphere at times," said Stephen Thomas, an assistant chief constable from Manchester, who is part of the British contingent working with German police. He credited police with knowing how to handle the crowds.

A large police presence helped deter trouble in opening-day host cities Munich and Gelsenkirchen.

In the western industrial city of Gelsenkirchen, Poland's 2-0 loss to Ecuador had prompted worries of Friday night hooliganism. Despite six fans from Germany and Poland being arrested for bodily harm, a police spokesman described the situation as more tranquil than a typical German soccer league game.

Saturday began in Gelsenkirchen with a far-right political rally.

About 230 supporters of the National Democratic Party were outnumbered by left-wing counter-demonstrators. Police separated both sides, though counter-demonstrators shouting "Nazis Out" managed to pelt NDP supporters with tomatoes. There were no arrests.

Such confrontations are routine in Germany — though in the run-up to the World Cup, a spate of attacks on nonwhites increased concerns over racism.

The rally "does damage Germany's image because of the World Cup," said counter-demonstrator Gerd Hebisch. "But you can see that there are at least 10 times as many demonstrating against their views — we don't want them here."