LONDON (July 2) - Twenty years after a scruffy one-hit wonder first demonstrated his gift for lofty dreams and grandiose statements, hundreds of the world's top performers and more than 1 million fans united for 10 free concerts across the globe aimed at fighting African poverty.

Bob Geldof claimed Saturday's shows would be ''the greatest concert ever,'' and it was hard to argue with him after the unprecedented gathering drew everyone from Snoop Dogg to Bill Gates, Mandela to Madonna.

But the ultimate success of the LIVE 8 extravaganza will be judged by whether the world's most powerful leaders, gathering next week for the Group of Eight summit meeting, listen to Geldof's demands for debt forgiveness, trade concessions and $25 billion in aid for Africa.

''History and the generations to come will judge our leaders by the decisions they make in the coming weeks,'' former South African president Nelson Mandela said after taking the stage in Johannesburg, where the crowd of more than 8,000 people gave him a five-minute ovation. ''I say to all those leaders: Do not look the other way, do not hesitate ... It is within your power to prevent a genocide.''

''This is our moment. This is our time. This is our chance to stand up for what's right,'' U2 frontman Bono told a crowd of 200,000 in London's Hyde Park.

''We're not looking for charity, we're looking for justice,'' Bono said. ''We cannot fix every problem, but the ones we can, we must.''

In Philadelphia, on the Independence Day weekend, actor Will Smith called the festivities a worldwide ''declaration of interdependence.''

''Today we hold this truth to be self-evident: We are all in this together,'' Smith said. Beamed around the world by satellite, he led the audience in snapping their fingers every three seconds, signifying the child death rate in Africa.

Paul McCartney and U2 opened the flagship show of the free 10-concert festival with a rousing performance of ''Sgt. Pepper's Lonely Hearts Club Band.'' A thunderous roar erupted from the crowd of about 200,000 as icons McCartney and Bono belted out the first line: ''It was 20 years ago today...'' - a nod to Geldof's mammoth Live Aid benefit that raised millions for African famine relief in 1985.

Bono, dressed in black and wearing his trademark wraparound shades, wrapped the crowd around his finger, enticing tens of thousands to sing along to the anthemic ''One'' and ''Beautiful Day.'' The crowd cheered when a flock of white doves was released overhead.

Geldof appeared onstage to introduce Microsoft billionaire and philanthropist Gates, whom the crowd greeted with a rock star's roar.

''We can do this, and when we do it will be the best thing that humanity has ever done,'' Gates said.

The crowd joined in as REM sang ''Man on the Moon,'' then heard U.N. Secretary-General Kofi Annan declare: ''This is really the United Nations ... The whole world has come together in solidarity with the poor.''

Geldof's claim that 3 billion people around the world were watching Saturday seemed overblown, as did talk in Philadelphia that a million people were on hand. But LIVE 8 was huge nonetheless, with a mile-long crowd stretching from the front steps of the Philadelphia Museum of Art and America Online saying that more than 5 million people sampled its live video streams, which broadcast all 10 concerts in their entirety.