American-Soviet relations are in their most precarious state in years, and the trend is pointing alarmingly downward, some of the most authoritative administration and Soviet sources are saying in private.

Soviet Foreign Minister Andrei A. Gromyko, before leaving New York on Friday for Moscow, came closer in public than any official on either side has done to point to the near-crisis in the making between the Kremlin and the White House. Of course, he gave the Soviet perception of it - or what the Soviet Union wants that perception to appear to be.

What is striking about the dilemma that now confronts Washington and Moscow is that professional diplomats on both sides agree that events during the past eight days have catapulted both nations into an extraordinary situation. And only inchoate portions of the dilemma have reached public consciousness.

"We are stumbling in very dangerous ground," one of the Carter administration's most experienced and unflappable policy planners said privately on Friday.

"It's a very precarious situation," he said somberly, "and nothing is orchestrated."

Perhaps they are being unduly alarmist, but they are not forecasting the imminent danger of a physical clash between the United States and the Soviet Union.

Yet they are not talking about just the impasse in the nuclear strategic arms limitation talks (SALT), or only the clash over Soviet-Cuban ventures in Africa.

Instead, more precisely, some of the most experienced diplomats on both sides are now registering, in private, extraordinary concern about the sharply descending curve in American-Soviet assessments about what each side is up to, globally. What each thinks the other is doing will determine major decisions to be made in the Kremlin, and in the White House, in the days and weeks ahead.

One of the most experienced senior American diplomats said yesterday:

"The Russians - and we - must join in limiting the potential damage. Nobody knows at this point where it will 'bottom out' . . . If we can arrest the damage , then we can talk about 'improving relations.' But that is certainly out of the question now. What we need now is 'damage control."

What suddenly happened since Gromyko met with Carter at the White ingly transformed the American-Soviet scene? What has caused Ameri-House eight days ago that has seem-can and Soviet diplomats, regardless of whether they are "doves" or "hawks," moderates or militants - "the professionals," as they like to call themselves - to join in concern, as one gloomily expressed it, that "events may spin out of control"?

Why is the administration this weekend drawing special attention to the American-Soviet focus of Carter's commencement speech on Wednesday at the U.S. Naval Academy?

And why is the White House so anxious to hint to the Soviet Politburo in particular, that is should wait to hear the Carter speech before rushing to conclusions - and decisions - about where U.S. policy is headed?

One answer is that nothing "suddenly" occurred. Instead, the accretion of three months of building tension was waiting at the White House like a simmering pot eight days ago when Gromyko entered early that Saturday morning. The water in the pot might have simmered down or boiled over. It boiled over.

What provoked White House anger to the boiling point was a one sentence remark by Gromyko challenging Carter's credibility. "Whatever you think you don't attack the president in his own backyard," a senior U.S. diplomat observed. "That wasunprofessional."

Interviews in New York and Washington during the last eight days with authoritative sources on both sides of the very tense American-Soviet divide help explain why "the professionals" are distraught about what may be ahead.

Tension between Moscow and Washington was building up week by week long before Gromyko reached the White House.

The Soviet Union, despite repeated American warnings, had started down what the administration regarded as the road toward direct, personal challenge of Carter on his highly prized campaign for human rights.

Yuri Orlov, one of the most industrious champions of human rights in the Soviet Union, had been given a maximum sentence of seven years, in a trial which western lawyers regarded as a travesty of due process.

Awaiting his turn for trial is Anatoly Scharansky, to whom Carter has tied his own credibility by publicly denying that Scharansky had any link to the Central Intelligence Agency, as the Soviet Union alleges. Putting Scharansky on trial on those charges automatically will put at risk Carter's own presitge - as Carter. Secretary of State Cyrus R. Vance, presidential national security adviser Zbigniew Brezinski, U.S. Ambassador to Moscow Malcolm Toon and other officials have notified the Kremlin.

Soviet-Cuban operations in Africa were arousing a tide of fervent anti-Soviet reaction across the United States, especially in Congress. Many of "the professionals" among American diplomats contend that Brezinski, constantly much closer than Vance "to the ear" of the president, is partly responsible for encouraging that reaction by his outcries about Soviet-Cuban adventurism in Africa, and by linking that alarm to the SALT negotiations, while officially disclaiming "linkage."

The four-year-old nuclear negotiations need no added burden of suspicion about Soviet intentions. Even without the uproar over Africa, SALT all along has been certain of a stormy run to ratification, which requires approval by two-thirds of the Senate. With a congressional election this year, and the burgeoning national suspicion about Soviet motives, SALT and the Gromyko-Carter talks were in a hazardous posture before Gromyko even reached Washington.

Gromyko was therefore "surprisingly restrained" on Wednesday, May 24, when Vice President Mondale attacked the Soviet Union that day before the United Nations special disarmament session. His "upbeat mood," as one official described it, prevailed when Gromyko met with Vance at the Soviet U.N. mission in New York the next day to pursue the SALT negotiations.

That same day Carter, in Chicago charged the Soviet Union's Marxist allies, Cuba and Angola, with direct complicity in the invasion of Zaire's Shaba Province, and warned that continued Soviet "abuse" of human rights, and the absence of "some constraints" on Soviet-China intervention in Africa "will make it much more difficult to conclude a SALT agreement and to have it ratified once it is written."

Three days earlier, in Peking, Brzezinski told his Chinese hosts: "Neither of us dispatches international marauders who masquerade as non-alligned (meaning Cuba) to advance big power ambitions in Africa . . ."

Nonetheless, when Gromyko addressed the U.N. on Friday he made a new overtune. He pledged that immediately after signing a SALT II accord, the Soviet Union would be ready to begin talks to seek "a substantial reduction" in nuclear arsenals - Carter's original goal.

At the White House meeting the next day came the private charge that "Gromyko lied" about Cuba's role in the Angola-based attack into Zaire. That meeting, both sides agree privately, went "rather disastrously." Gromyko, however, tried to muffle the discord in his initial remarks to reporters.

The Soviet foreign minister's diplomatic lapse was his challenge to the credibility of the administration's "informationa" on the Soviet-Cuban role in Africa.

In the crossfire that followed that Saturday Vance and Gromyko decided on an emergency meeting Wednesday in New York to try to arrest grave damage to the entire state on U.S.-Soviet relations. Then Brezeinski's television interview last Saturday virtually foredoomed diplomatic repairs, for he doubled the American accusations, charging the Soviet Union with grossly violating the "code of conduct" for detente.

Not surprisingly, the Gromyko-Vance meeting in New York Wednesday barely succeeded in preventing total blockage of the evenue of communications.

The Carter outcry two days ago against a Washington Post report that his administration had "effectively forzen" the SALT negotiations was aimed at a larger target than a newspaper, as Carter himself acknowledged.

Carter was attempting to convince Leonid I. Brehnev and the Politburo that he is not abandoning the SALT treaty, which seriously ailing Brezhnev long envisioned signing at a summit conference in Washington this summer to climax his career. But Brezhnev knows better than any other outsider the actual state of the SALT negotiations.

In sum, this is why great anxiety is now bedeviling all the diplomats about the upredictable sequence ahead.