The United States and Russia, each making concessions to strike a deal, will scrap two-thirds of their deadliest weapons under the most far-reaching nuclear-arms-reduction accord in history.

All land-based missiles with multiple warheads will be dismantled by the year 2003, and the U.S. Navy, shielded until now from having to scale back, will lose a sizable chunk of its nuclear arsenal.The two countries also agreed Tuesday to work out a system to guard against ballistic missile attack. Other countries will be in

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vited to participate.

Together, the United States and Russia currently have more than 20,000 long-range warheads. The agreement announced by Presidents Bush and Boris Yeltsin will cut them down to between 3,000 and 3,500 on each side.

The sweep of the agreement exceeded most expectations. A desperate 11th-hour race to conclude it at the summit contributed to the drama.

"With this agreement," Bush said, "the nuclear nightmare recedes more and more for ourselves, for our children and for our grandchildren."

The cuts are to be carried out in two phases and go far beyond the one-third reductions in long-range weapons required under the new Strategic Arms Reduction Treaty.

That accord, still to be ratified by the Senate, took nearly a decade to negotiate with the Soviet Union. The new agreement was reached in only five months.

Even in the final hours, Secretary of State James A. Baker III was saying he did not know if an agreement was possible and that several extraordinarily tough issues were defying resolution.

"Our ability to reach this agreement so quickly is a tribute to the new relationship between the United States and Russia, and to the personal leadership of our guest, Boris Yeltsin," Bush said at a White House Rose Garden ceremony.

The United States set out to remove the backbone of Russia's nuclear strength - land-based missiles with multiple warheads. That goal was achieved.

But to get there the Bush administration made two significant concessions: It agreed to establish an overall ceiling of 3,000 to 3,500 warheads, much deeper than the 4,700 Bush had proposed.

And while the president offered in January a one-third cut in the ballistic missile warheads on nuclear submarines, the agreement provides for a 55 percent reduction.

Sen. Joseph R. Biden Jr., D-Del., praised Bush for trading cuts in U.S. submarine warheads for a ban on land-based missiles with multiple warheads.

"By focusing on eliminating as many nuclear weapons in the former Soviet Union as possible, as fast as possible," Biden said, "the president has struck what may be the best deal in the history of arms control."

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Biden, chairman of the Senate Foreign Relations European subcommittee, said the next step should be to call on Britain, France and China to freeze their arsenals with a few hundred weapons each in exchange for further cuts by the United States and Russia to a ceiling of 1,000.

The only multiple-warhead missiles that will remain in the American and Russian nuclear arsenals would be those based on submarines. However, both sides would have to cut back - the United States from its current level of 3,840 and the Russians from their 2,320.

Overall, the two superpowers would be permitted no more than 3,000 to 3,500 strategic warheads each. But U.S. officials, briefing reporters under rules that barred identifying them, said the Russians would choose 3,000 and the United States 3,500.

The agreement will be put into a treaty document within three months, signed by Bush and Yeltsin, and then submitted to the Senate and to the Russian parliament for approval.

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