Nuclear weapons and how to control them are the centerpiece of Walter Mondale's diplomatic and defense proposals. ''Nowhere else is Mr. Reagan's record more appalling and more unacceptable,'' he says. ''We have an extremely dangerous and escalating arms race.''

In some ways, Mr. Mondale does not differ with the incumbent. He has not renounced the ''first use'' of nuclear weapons in Europe should NATO countries be overrun by Warsaw Pact troops. And his running mate, Geraldine Ferraro, made clear in a steely-eyed response during her debate with Vice-President George Bush last week that she would not hesitate to order ''swift, concise, and certain retaliation'' should the Soviet Union launch a nuclear first strike against the United States.

Mondale and Ms. Ferraro also support new Trident submarines with nuclear missiles, the ''stealth'' bomber, air- and ground - launched cruise missiles, and the single-warhead mobile intercontinental ballistic missile dubbed ''midgetman.''

But the thrust of Mondale's arms control philosophy and the steps he promises are far different from those of Reagan.

He has challenged Moscow to ''temporary, mutual, and verifiable moratoria in several areas.'' This ''quick freeze'' would include a halt to the testing and deployment of all weapons in space (including antisatellite devices); underground nuclear testing; new ballistic missiles now under development; and sea-launched nuclear cruise missiles.

In essence, Mondale says that on the day he takes office, the US will ''pause'' in these areas and start again with such testing and deployment only if the Soviet Union does. He also promises within six months to hold a summit meeting with Soviet leaders ''to reduce tensions and explore possible agreements ,'' and to engage in annual summits.

Mondale is not specific about how he would propose to reduce strategic nuclear weapons, except to say that he would seek ''deep cuts'' within the framework of the second Strategic Arms Limitation Treaty (SALT II). On intermediate-range nuclear forces, he would ''repropose'' the ''walk-in-the-woods'' draft accord, which was worked out privately by US and Soviet negotiators and rejected by Moscow. This would reduce the deployment of US missiles in Europe in exchange for cuts in Soviet SS-20s now aimed at NATO countries.

Mondale also promises to uphold the Anti-Ballistic Missile (ABM) Treaty, which some experts warn could be undercut by the Reagan administration's push for space-based missile defenses. He wants to establish ''nuclear-risk reduction centers'' in Washington and Moscow. Mondale will ''renew the fight against nuclear proliferation,'' he says, and reopen talks on a comprehensive nuclear test ban treaty.

Negotiations to ban all nuclear weapons testing (now limited to underground explosions) have not progressed since Reagan took office. Mondale charges that Reagan has ''weakened the intellectual and political leadership for sensible arms control'' by putting ''amateurs and ideologues'' in charge.

The Democrat says he would increase the budget for the Arms Control and Disarmament Agency and assign to it ''bright and experienced leaders who know how to encourage the generation of new ideas.''

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