At one time, the eight world leaders who gathered this weekend beside Birmingham's colonial-era canals might have been called "the most powerful men on Earth."

They sure don't look like it now.

With a new nuclear arms race exploding in South Asia, a fiery uproar in the streets of the world's fourth-largest country and the planet's poorest residents sinking deeper into poverty, the leaders of the Group of Eight industrial democracies looked deeply at all these problems -- and pronounced themselves "frustrated."

"We are both concerned and frustrated," said the summit's host, British Prime Minister Tony Blair, when asked after the closing session today about the group's apparent inability to influence India and Pakistan. "There's a sense of frustration about it, yes, but there's also a determination that we have a strategy to deal with it."

The stunning news from India -- that the world had gained its sixth declared nuclear power -- hit the headlines just four days before the leaders arrived for their annual meeting.

The eight discussed the new crisis at length. They issued wordy communiques. They joined in a heartfelt chorus of "All You Need Is Love" at a rock concert. But they were unable to agree on concerted action to stop India or Pakistan from going their own way on nuclear weapons.

The statement that emerged from the group was written in vague language to disguise serious disagreements over whether to apply economic sanctions against India or to threaten them against Pakistan. "India's relationship with each of us has been affected by these developments," the closing communique said. Blair explained that this means "individual countries will have to make their own individual responses" to India's nuclear arsenal.

Japan has called for strict economic and political sanctions against India, and the United States has urged a similar response. But the other G-8 countries were inclined more to verbal warnings, or mild reprimands, of India.

One problem for the G-8 leaders when they preach against nuclear proliferation is that half of the countries around the table -- the United States, Britain, Russia and France -- are themselves nuclear powers. It was just three years ago that France was the target of global denunciation for staging its own nuclear tests.

In 23 years of summits, the group of rich industrial nations has changed little, while the rest of the world has changed a lot. The G-7 was formally expanded this year to a G-8 with the inclusion of Russia -- another essentially European power. But the group includes no nation from the Southern Hemisphere. Its Asian member, Japan, is hardly the country that most of its regional neighbors would pick to represent them on the world stage.

Most of today's Final Communique was written by mid-level bureaucrats before the heads of state even arrived here, although the leaders did quickly append a section on the financial crisis and fatal rioting in Indonesia.

Summit defenders say it is obviously valuable to have world leaders get together now and then and spend personal time together. "If we don't meet, we can't discuss these things," Canadian Prime Minister Jean Chretien said today. "Some of the progress comes year after year. . . . If you don't have discussion you don't have progress."

The G-8 can claim progress this year on issues such as international crime, Internet commerce and the Year 2000 bug that may be imperiling the world's largest computers. The annual meeting also provides a global stage for interests and movements to illuminate their own issues.

This year, in fact, a massive demonstration on the issue of Third World debt prompted the G-8 to issue a formal statement on debt relief -- although this proved to be another topic that left the leaders well short of agreement.

The G-8 countries generally applaud the annual get-together, if for no other reason than that it enables leaders from the member nations to develop a personal rapport that can help hold them together in times of crisis. But there are now a profusion of these high-level gatherings -- in addition to the annual G-8 meeting, the U.S. president is obliged to attended regular summits with leaders from the Asian-Pacific nations and leaders from South America.

By now, even champions of the process admit to summit fatigue. "The only thing I'm against," White House national security adviser Samuel R. "Sandy" Berger declared, "is adding any more summits to the agenda."