Now that Soviet President Leonid Brezhnev has signaled his readiness to talk about reducing strategic nuclear arms, American officials are grappling with thorny technical and political problems that need to be overcome if there are to be meaningful curbs on the arms race and an increase in security for both sides.

Perhaps the key issue is whether the superpowers will find a way to restrain themselves from fielding still more nuclear-tipped missiles over the course of negotiations that could take many years. The deployment of such weapons could destroy the negotiations.

This is an especially difficult problem for the United States. The Reagan administration, claiming that Moscow is superior in missile power, has set out to modernize American forces by pressing ahead with development of the new MX land-based missile, Trident II submarine-based missile and several new air, land and sea-launched cruise missiles.

The most deadly elements of this new striking power--the highly accurate MX and Trident II missiles--will not be ready for deployment until the mid-1980s, but the key question for planners of the arms talks is how to keep the Soviet Union from further building up its forces while the United States is proceeding with plans for a buildup.

Further complicating the problem is the probability that Moscow can add to its forces much faster than can the United States.

The Soviets already have newer and bigger land-based missiles, to which they could add warheads.

Intelligence sources say the Soviets have developed, but not yet tested, two new solid-fuel missiles that could be put into production quickly. One is a medium-sized weapon that could be the successor to the current SS17 or SS19 missile. The other is a smaller, mobile, long-range missile that could be a successor to the SS16, banned by the strategic arms limitation treaty signed in 1979 but never ratified by the Senate.

High-ranking administration officials say the question of restraining Moscow during arms negotiations is an important one, but it is "too early" to answer it in public. Some officials say, however, that the administration is discussing what are termed "mutual interim restraints" as gestures of goodwill during negotiations.

Critics of the Reagan administration's approach to arms control argue the United States could put a ceiling on Soviet missile and warhead numbers by ratifying the SALT II agreement, signed by Brezhnev and then President Carter in 1979. Then, they argue, negotiations under Reagan's plan, called START, could begin for deep reductions from those ceilings. But the administration has rejected that idea, arguing that SALT would formalize the big Soviet lead in heavy missiles and reduce Moscow's incentives to negotiate further.

President Reagan's START proposal calls for sharply scaling back each side's forces to no more than 850 land- and submarine-based missiles (the United States has roughly 1,700 and the Soviets 2,400) and limiting to 2,500 the number of warheads that can be mounted on land-based missiles. The idea is to force reductions in land-based missiles--which are the most accurate, most threatening and also the most vulnerable to attack. That combination also makes them most worrisome and, considering that Moscow has its biggest edge in this category, explains why Reagan wants to limit them first.

But the administration has not publicly answered critics who claim that even cutting back to 850 missiles and 2,500 land-based warheads will not remove the threat of a disarming first strike by the Soviets and could even leave Moscow with enough left over for a strong second strike. It is this fear of a disarming first strike that drives the arms race.

Rep. Albert Gore Jr. (D-Tenn.) first raised the issue in congressional hearings two weeks ago, and it has been echoed by many specialists outside the administration since then. Gore said in an interview that even if the United States, under a future arms pact, deployed only 200 MX missiles and 300 existing Minuteman missiles on land, Moscow would still be able to hurl two or three warheads from land-based missiles against each of those targets and still have enough left for a second strike.

The closest thing to a public answer has come from Fred Ikle, an undersecretary of defense who told reporters that such calculations are premature because they really depend on how the United States deploys its forces. This means that if the United States finds a way to deploy the MX which makes it hard for Moscow to hit, the threat of a first strike will be reduced.

Thus far, the Pentagon has not been able to figure out where to put the MX to keep it safe, although a new scheme called "Dense Pack" is beginning to get high-level attention. This calls for MX missiles to be based in tight clusters so that incoming atomic warheads would destroy each other rather than the MX missiles protected in underground shelters. Other schemes could involve building an anti-missile defense system.

Other top officials say privately that reduction of the first-strike threat was "an essential aspect" of the calculations that went into the president's proposal. But under further questioning, and without being specific, they acknowledge that the proposal does not entirely solve the vulnerability problem.

Another tough technical problem involves verification of any treaty, especially how to verify the number of warheads on land-based missiles and whether cruise missiles are armed with nuclear or conventional warheads. Some Reagan administration officials remain suspicious of what the Soviets are doing under the SALT II restrictions, which are still being informally obeyed. However, sources say the administration refuses to bring complaints before the Standing Consultative Commission, whose meeting it attends, for fear of legitimizing SALT II.

Brezhnev, who has not yet given a formal reply to Reagan's May 9 call for arms talks to begin, criticized Reagan's proposals in a speech Tuesday in Moscow, and advocated a nuclear freeze, which is popular in western Europe but not in the White House. But his speech did not lock Moscow into hard positions, and is being interpreted here as "relatively restrained in tone," as one top official put it.

Thus officials here expect the talks to begin and see some basis for negotiations.

If the START talks are lengthy, there may be yet another complication: new leadership in the Kremlin. Soviet leader Brezhnev is 75 and has been ailing for several years.

In Washington, meanwhile, there seems to be some kind of a plan under way both to add validity to the START proposals and to bolster Reagan's image as a president thoroughly on top of national security issues.

In a speech last week, Reagan's friend and new national security adviser, William P. Clark, repeatedly emphasized the president's "extraordinarily active role." Some administration officials are known to feel that Clark's tone was too overtly defensive.

Another high-level administration official also volunteered to a small group of reporters in a recent meeting how "seriously engaged" the president was in the START decisions.

Asked why the president seems to have trouble at press conferences with questions about the subject, the official said, "I can't answer that. He's not familiar with a lot of the jargon . . . but he's very perceptive about the logic and analysis that backs it up."