Once or twice a week, in the windowless situation room of the White House basement, the men who have become the Reagan administration's arms-control brain trust huddle around a large oblong table to ponder U.S. strategy and tactics. It is a group dominated by skeptics who generally agree that past arms-control agreements were gravely flawed, and who share an anxiety about the need to look tough to the Soviet Union.

And it is a group divided by well-masked personal animosities.

As one of the highest councils of government, these men officially form the Special Arms Control Policy Group (once known as SACPG, pronounced "sack-pig," it is now SAC-G, or "sack-gee").

Although the men of SAC-G are theoretical equals in shaping U.S. policy, some are more equal than others. Some, in fact, despite positions of prominence in the government, wield little influence and are fundamentally figureheads. And as with sensitive groups such as this in all administrations, the members closest to the president are the most powerful. It is in SAC-G that the rifts within the administration on the future of arms control should be most vigorously evident.

But in this group, devoid of any enthusiastic arms-control zealots, even the suspicion of flexibility in bargaining with the Soviets can taint a viceroy's standing among SAC-G's most rigid hard-liners, according to some officials.

Consequently, advocacy of compromise with the Soviets by the few Reagan officials who believe in it has become something of a parlor game in Washington, promoted in off-the-record conversations with journalists and members of Congress or informal exchanges between like-thinking colleagues.

"Don't mention my boss' name," pleaded one deputy interviewed for this article. He noted that Paul H. Nitze, special adviser to the president on arms control, had been described in a recent U.S. News & World Report article as a proponent of flexibility and "it's affected his credibility" with the president.

Bureaucratic infighting has long been part of arms-control policymaking. In the past few administrations, open feuding among the State and Defense departments and the National Security Council has been common.

That battling continues under President Reagan, confirming the diplomatic bromide that the toughest negotiation in any arms-control agreement takes place in Washington within the government rather than with the Soviets. But in the Reagan administration, the internal battles have been easier, because this government has never moved beyond positions that were unacceptable to the Soviets. The Soviet government has played the same game, offering only unacceptable proposals to the United States in the last five years.

The predilections of SAC-G come straight from the boss. Reagan swept into office in 1980 having opposed every past treaty with the Soviets and vowing to resist pressure to negotiate with Moscow, an attitude he modified in the face of congressional and European demands.

"No one is going to lose any sleep in this administration on the issue if they fail to reach agreement," said one arms-control expert who regularly meets with the Reagan strategists.

Overhanging the Reagan administration's deliberations on arms control is a new element introduced 2 1/2 years ago when the president unveiled his Strategic Defense Initiative, the so-called "Star Wars" research program to try to find a way to destroy incoming nuclear missiles. Preserving Reagan's SDI dream of a technological Astrodome over the western world has become an acid test for loyalty within the administration.

"There's quite a taboo to be seen to be sympathetic toward any arrangement that might circumvent or subvert the president's idea of an SDI shield," one recently retired official said. "The taboo doesn't inhibit a lot of intelligent research and discussion within agencies. But it does inhibit a purposeful interagency discussion even on a transition [from the current dependency] on offensive weapons to a strategy of both offense and defense ."

Given the sanctity of SDI, it may be understandable that one senior Defense Department official likens himself and his Pentagon colleagues to "Horatius at the bridge," battling others who want to "sell out" Reagan's dream.

Across the Potomac River at the State Department, these Pentagon officials are deplored as "know-nothings," although many of the arms-control experts in Foggy Bottom admit they have not dared to carry to the president's ears their departmental conversations on restraints on SDI.

The fear of being tagged as a Star Wars nay-sayer has stifled the traditional public airing of deep disagreements in the Reagan administration. In fact, officials with reservations about SDI can be found in every relevant agency. They have provided a stream of "background" assurances to members of Congress and journalists promising that in response to the right sort of Soviet offer, officials like Secretary of State George P. Shultz, national security affairs adviser Robert C. McFarlane and Nitze will go to the president and argue for restraining SDI. But this has not happened. One arms-control expert who has worked with the Reagan team says it never will, because "those men are moderates, and moderates don't fight for their convictions."

This muting of debate is a new wrinkle in the Reagan presidency. In the early 1980s, disagreements between State and Defense officials on strategic and intermediate-range nuclear missile negotiations were visible in embarrassing detail, thanks largely to Time magazine correspondent Strobe Talbot, who documented the process in a book, "Deadly Gambits."

In part to prevent another such book, the lid is tightly battened. White House and State Department public affairs officials refuse to confirm the membership of interagency groups, such as SAC-G, or even when they meet. More importantly, the members of SAC-G now seem considerably more reluctant to divulge details of their deliberations.

The chairman of SAC-G is McFarlane, a former Marine Corps lieutenant colonel. A former member of the Senate Armed Services Committee staff, he has not assumed the powers of a Henry A. Kissinger. Instead, in arms-control matters, he has been more of a staff coordinator, making his views known privately but subordinating them in attempting to create the consensus he knows the president wants.

Supporting McFarlane from the National Security Council recently have been Jack F. Matlock Jr., a Foreign Service Soviet expert, and Ronald F. Lehman II. Lehman, who handles arms-control matters for the NSC, is another of the many alumni of the Senate Armed Services Committee staff who sit around that table in the situation room. Now he is attached to the U.S. delegation to the Geneva negotiations.

The Pentagon is always a weighty presence on such panels, a fact of life reinforced in this administration by the president's close friendship with Defense Secretary Caspar W. Weinberger. As one official characterized the relationship, "Weinberger voices Reagan's inner thoughts."

Weinberger's principal assistant on SAC-G is Undersecretary for Policy Fred C. Ikle, who was director of the Arms Control and Disarmament Agency from 1973 to 1977. But the Pentagon's most forceful representative in the group is Richard N. Perle, assistant secretary of defense for international security policy. Perle came to the administration from the Senate, where he served for years as aide to the late senator Henry M. Jackson (D-Wash.), who militantly fought in the arms-control debates of the '60s and '70s for a harder line toward Moscow. Participants in this process agree unanimously that Perle is the most effective member of the group, combining detailed knowledge with a clear sense of direction and unfailing self-confidence.

Supporting Ikle and Perle are a squad of like-minded young lieutenants, such as deputy assistant secretaries Frank J. Gaffney Jr. and Douglas J. Feith, both also members of the Senate Armed Services Committee "mafia."

The Joint Chiefs of Staff also hold a SAC-G seat, giving the Pentagon another voice at the table. In the early years of the Reagan presidency, the chiefs, who as a body had supported the SALT II arms limitation agreement with the Soviets, appeared to back some State Department initiatives that were opposed by Defense Department civilians.

More recently, according to sources close to the panel, the chiefs' position has become ambiguous as they provide statistical fodder but sidestep political issues. Today, with Vice Adm. Curt S. Moreau Jr. and Commodore Dean R. Sackett Jr. representing them at the table, the chiefs incline to Weinberger's line, according to one official.

The State Department SAC-G representatives are newcomers: Deputy Secretary of State John Whitehead, an investment banker who began government work this summer, and H. Alan Holmes, a career diplomat and former ambassador who has been director of the office of politico-military affairs for only two months. Although Holmes once worked on NATO issues in the State Department, neither he nor Whitehead have much arms control experience.

Their boss, Shultz, has shied away from the details of arms control, relying instead on top aides. In the past, that task fell largely to Richard R. Burt, a former think-tank expert on nuclear strategy and New York Times reporter, who had Holmes' job before becoming assistant secretary for European affairs. This year Burt was moved out of the arms control loop and sent to Bonn as the new U.S. ambassador.

Earlier this year, Nitze moved to the State Department as coordinator of arms control policy and SAC-G participant after his stint as a negotiator in the intermediate-range missile talks in Geneva.

The veteran negotiator, 78, also serves as special adviser to the president, a title intended to give Nitze added stature in the interagency forum. But his role now seems somewhat diminished, in part because of the reputation as a compromiser that he earned during the Geneva talks in the first Reagan administration, and also because of personal factors such as his wife's illness.

Backup support at the State Department is supplied by a clique of career officials who have wrestled with arms control for years. Considered most knowledgeable among them is James B. Timbie, a physics PhD who joined ACDA in the Nixon administration before moving to State last year following service as Nitze's deputy in Geneva.

Because Timbie and the other careerists worked on the past treaties Reagan found offensive and are considered "soft" on the Soviets, they have become targets for Reagan appointees in the Pentagon. Consequently, they tend to hug the bureaucratic terrain, keeping a low profile and avoiding interagency spats.

ACDA was established in the Kennedy administration as the official advocate of arms control. Under current director Kenneth L. Adelman, the agency has generally beat the drum publicly for whatever policies the administration has endorsed.

Recent ACDA initiatives included inviting Soviet scientists to attend a U.S. underground nuclear detonation in hopes of a reciprocal invitation from Moscow. The agency also floated the notion that the United States should emphasize ambiguities in the SALT II treaty limits and place a Poseidon submarine in drydock rather than dismantling it as the treaty requires -- and as Reagan decided to do.

The Central Intelligence Agency representative at SAC-G recently has been assistant director Clare George, according to one source. George usually limits himself to technical analyses, leaving policy arguments to CIA Director William J. Casey, who takes his views directly to Reagan, as does Weinberger.

When they are in Washington, the three ambassadors to the Geneva talks take part in the SAC-G discussions. They are Max M. Kampelman, a longtime Democrat and Washington lawyer; John G. Tower, former chairman of the Senate Armed Services Committee, and Maynard W. Glitman, a career Foreign Service officer who has served in the Pentagon and as a Nitze deputy. Sources said the trio is not particularly influential in making policy, although Kampelman and Tower show great prowess on Capitol Hill defending the policy.

The surprise to arms-control experts has been Tower, who reportedly pushed the strategic arms discussions forward while cultivating an easy, diplomatic rapport with the Soviets.

The product of the SAC-G deliberations, either new positions or instructions to the negotiators, goes to the National Security Council. In practice, however, final policy choices are usually made in a conclave of Weinberger, Shultz, Casey and McFarlane with Reagan.

But this group seems in no hurry. They are waiting for the Soviet Union to make the first bold step away from the current superpower stalemate.

Recent events have been revealing. Earlier this month several of Reagan's key aides, including members of SAC-G, were hinting at possible flexibility on the question of trading restrictions on SDI for substantial reductions of offensive forces. But in his news conference Tuesday night, Reagan ruled out such a bargain.

The next morning, however, some of the same individuals who had suggested Reagan's flexibility were insisting that the president's statements were not final, but rather a bargaining strategy to up the ante on SDI. At the Pentagon, on the other hand, there was considerable enthusiasm for the president's declarations.

It was not the first time that the Pentagon had the last word, and the last laugh -- something that could happen again before the November summit.

Last July, when Reagan decided to adhere for the time being to the unratified SALT II arms-control agreement by dismantling a Poseidon submarine, making room under the SALT II limits for a new Trident sub, the Pentagon was assigned to do a new study of Soviet treaty violations and the military responses that should be taken by the United States.

Perle controls the study, and it has taken on a broader scope. Perle's analysis will provide a Pentagon view of the nuclear balance and the projected threat of Soviet strategic offensive and defensive programs. These will be measured against presently planned U.S. military programs. Perle and his colleagues will propose what they consider appropriate responses to meet the Soviet threat.

Fliply named the RSVP study, for responses to Soviet violations policy, it will be ready before the original Nov. 15 due date, and thus well before the Nov. 19-20 Reagan-Gorbachev meeting, so it can be put "into the pre-summit mix," as one Pentagon official put it.

The report's sharp attack on Soviet policies and calls for new U.S. weaponry "will be the perfect sendoff" for Reagan, the Pentagon official said. For State Department officials who want the pre-summit days to emphasize possible improvement in superpower relations, he added, "The study will be like a obscenity in the punchbowl."