The Navy is moving full speed ahead on a new weapons system that the admirals love but some arms controllers are concerned about: deployment of long-range cruise missiles on scores of ships and submarines.

The arms controllers are wary of the project even though the missiles, as now authorized, would carry conventional rather than nuclear warheads.

Over the next decade, the Navy plans to build 3,500 to 4,000 Tomahawk cruise missiles -- small, pilotless jet-powered craft that have short wings and look like flying torpedoes -- and install them on submarines, destroyers and cruesers as well as on two old battleships being taken out of mothballs.

They will be designed to strike both enemy shipping and targets deep inland, such as air bases between Moscow and Leningrad from which Soviet Backfire bombers might launch attacks against the U.S. fleet. w

Under the plan described by two Navy experts, Adms W. A. Williams and John Dixon, these missiles would have a range of 700 to 1,100 miles when launched from surface ships, and 500 to 700 miles when popped out of the torpedo tubes of submerged submarines.

So far, the Pentagon has only proposed and Congress has only approved production of missiles that would carry conventional warheads; these would be roughly equivalent to 1,000-pound bombs. A nuclear-tipped version is under consideration, say the admirals, and funds are available to keep that option alive even without a production decision.

The potential problem for arms control, as the admirals acknowledge, is that the conventional and the nuclear-armed missile, if the latter is ever deployed, are virtually indistinguishable.

This difficulty, plus the sheer number of missiles planned for deployment, could pose an insurmountable verification problem if such weapons were to be included in future arms control negotiations.

Though some senior defense specialists say there could be an effort to make the two versions identifiable, there is a widespread feeling that cruise missiles will mark the beginning of the end of arms control verification of the kind provided for in the previous strategic arms limitation agreements between the United States and the Soviet Union during the 1970s.

Under the original 1972 SALT I treaty, each country relies on its own national mens of verification, which means picture-taking satellites, to count the number of missile "launchers" deployed by the other side. With cruise missiles aboard ships and submarines, such counting would be virtually impossible.

Cruise missiles, advertised as being extremely accurate so that conventional warheads can be used against many targets instead of nuclear bombs, respresent an area of technology in which the United States is though to have a significant lead over the Soviets.

The weapon, therefore, is cherished by the military, especially the Navy, but also by the Air Force which is scheduled to deploy thousands aboard B52 bombers and the successor to the B52, which is expected to be the B1 bomber.

Adm. Dixon, the Navy's director of strike and amphibious warfare, argues that conventionally armed cruise missiles, and possibly nuclear-armed missiles later on, basically enhance the ability to strike maritime targets that were previously invulnerable or could be hit only at high risk by manned aircraft. Similarly, he says, they give virtually all ships of the fleet the offensive power to hurt the enemy badly.

Adm. Williams, director of strategic and theater nuclear warfare, adds that a nuclear version at sea would prevent the Soviets from trying to wipe out, in a preemptive strike, the entire U.S. and allied local nuclear striking power in Europe.

Williams argues that such Navy weapons, therefore, would simultaneously add to the range of possible responses to a Soviet attack in Europe and help deter such an attack.

On July 10, the Navy test-fired a Tomahawk for the first time from a submarine well off the California coast to a land target almost 400 miles away. The test, the Navy said, was successful.

The first submarine-launched missiles, which are meant to hit land targets, are expected to become operational in January, 1982, according to Dixon. The submarine-launched anti-shipping version is slated for June, 1982, and a 1983 date is set for initial deployment of both land-attack and anti-shipping missiles aboard surface ships.

The SALT agreement, signed in 1979 by then-president Carter and Soviet leader Leonid I. Brezhnev but never ratified by the U.S. Senate, contains a protocol which prohibits deployment of land- and sea-based cruise missiles with a range greater than 375 miles.

That protocol expires, however, at the end of this year, and is virtually certain not to be renewed, since there are no new SALT discussions going on between Moscow and the Reagan administration. Therefore, by January thee will be no constraints on the cruise missile programs.

The body of the main SALT II agreement, which both countries continue to observe in a de facto sense, does require that B52 bombers equipped to carry long-range, air-launched cruise missiles be counted in the overall limitations of the treaty.

The U.S. Air Force missiles carry nuclear bombs in the nose. The treaty, however, has never been clear on distinctins between conventional and nuclear-armed versions of the same weapon, in part because the situation did not arise until the multi-purpose cruise missile arrived.

As far as the Navy is concerned, SALT doesn't apply to conventional-warhead weapons, even though they are hard to distinguish, visually, from the nuclear-tipped.

Navy Secretary John Lehman has also publicly expressed the view that there are no legal requirements for the United States to abide by SALT any longer.

Some officials from previous administrations suggest privately that, apart from the utility of cruise missiles as military weapons, the fact that they complicate future arms control is another reason the Navy and Lehman are so high on them.