An extraordinary series of speeches by leaders in Moscow and Washington in recent days--speeches that contain elements of both conciliation and confrontation--may reflect the beginning of a new phase in the tense relationship between the superpowers, according to specialists and U.S. officials.

No one can be certain where this could lead, the specialists said. And there is no sign, as Secretary of State George P. Shultz made clear in a major statement to a Senate committee Wednesday, that any breakthrough with Moscow is near.

But the sudden outpouring of statements from both capitals and their dual nature continued yesterday, reinforcing the idea that both nations may be struggling more than in recent years for a way to stay tough but ease tensions

At the State Department yesterday, spokesman Alan Romberg issued a sharp rebuttal to a speech on Thursday by Soviet Foreign Minister Andrei Gromyko which was predominantly critical of the United States but which contained a few nuggets of conciliatory language.

Romberg said Gromyko "didn't offer much encouragement about Moscow's readiness to engage in a constructive search for ways to ease East-West tensions" as Shultz has urged. And he accused Gromyko of "misrepresenting the position of the United States on virtually every issue."

But Romberg also said "we, of course, welcome Gromyko's assertion that the U.S.S.R. seeks smoother relations with the United States," adding that Washington would judge the significance of Gromyko's statement on the basis of Soviet actions rather than words.

At another press conference here yesterday, two leading U.S. experts on Soviet affairs, William G. Hyland and Dimitri K. Simes, suggested that Soviet President Yuri V. Andropov's recent consolidation of authority and President Reagan's success at home and with the allies on security issues might "open the door for negotiations" on both sides, as Simes put it.

The two specialists differed, however, on the prospects for an arms control agreement, one key measure of how things stand.

Simes, a Moscow-educated foreign policy specialist who came to this country in 1973, and Hyland, a national security adviser to President Ford, spoke to reporters at the Carnegie Endowment for International Peace, a private research organization where both are senior associates.

Simes said domestic politics in both capitals could inhibit progress on arms control.

Although Andropov appears strengthened, Simes forecast he will be preoccupied with the troubled Soviet economy and controversial new economic reforms. The Soviet leader, he said, is therefore not likely "to overload the political circuits at home" by also moving soon toward an arms agreement that might also be controversial in leadership circles recently reinforced by more members of the Soviet military-industrial complex.

In Reagan's case, Simes said the success at home and with allies of his recent statements on military issues and flexibility in arms control--and Shultz's recent statement on U.S.-Soviet relations--could ease pressure on the administration to bring real flexibility to the bargaining table.

Hyland said U.S.-Soviet relations are "more fluid now" than at any time since the beginning of the Reagan administration, with many "straws in the wind" that could lead to progress.

Hyland viewed the Gromyko and Shultz speeches as essentially setting the agenda of concerns for both countries: tough statements containing the seeds of accommodation "to move out on."

"I see the two sides, for the first time really, at least beginning to move along parallel tracks," Hyland said. "Relations now are moving to a different phase, a phase with much more possibilities for maneuver and for more serious negotiations than there has been in almost three years."

Hyland and Simes had high praise for the 35-page Shultz statement on policy toward Moscow. Hyland called the presidentially approved document a "watershed, a turning-point in the Reagan administration approach" in that it recognized the need to make a clear statement on U.S. expectations to a new Soviet leader.

While the statement reflected the traditionally tough and skeptical Reagan approach to the Soviets and demanded Soviet restraint in many areas, Hyland focused on Shultz's assertion that the administration had effectively "begun to rebuild our strength" and thus "we now seek to engage the Soviet leaders in a constructive dialogue . . . ."

Privately, other administration and State Department officials also point to this as a key message to Moscow. One top aide to Shultz yesterday summed up his boss's message this way: "We've got our feet on the ground now. We've managed to sort out how we view the Soviets and we have gathered the confidence to probe them."

Hyland said that if the Russians read Shultz's statement "carefully, I think they will see a lot in it that is mainstream Soviet-American relations" rather than the harsher rhetoric Reagan has used on other occasions.

He also noted that Gromyko, while making a tough speech about Moscow's views, also urged that "the truly historic opportunity" that presents itself in arms control not be allowed to "slip by."

Hyland called attention to other passages in Shultz's speech that reminded listeners that the Soviets have, in the past, made important foreign policy shifts in the aftermath of leadership transitions.

Hyland said he found the Soviets on the defensive these days, "in a semi-ugly mood," with serious problems at home, in Poland and elsewhere in eastern Europe. Simes agreed, adding that Washington had also put Moscow on the defensive, but suggested such defensiveness was not necessarily an advantage in dealing with the Russians.

But Hyland said he sees a convergence of events that could at least open the door for progress in arms control, possibly within the next year. These include the strengthening of Andropov and Reagan at home, the approach of a presidential election here and acceptance of the notion that Reagan is ready for serious negotiations after resisting them for three years because he believed he needed to build up U.S. strength first.

Hyland said he sees the recent reelection of conservative leaders in West Germany and Britain (and the probable electoral success later this month of the pro-U.S. regime in Italy) as also reducing Soviet chances to split the North Atlantic alliance. He said the same recognition must be sinking in in Moscow. Those three countries are to receive new U.S. Pershing II and cruise missiles in December unless an arms agreement is reached before then in companion talks in Geneva on intermediate-range missiles.

Simes said Moscow is not apt to give Reagan an election bonus next year by being accommodating on arms. Progress, if it comes, may have to wait until 1985 or later, he said.

Both specialists said that the immediate key to the relationship, arms control and a possible summit meeting, lies in what happens at the Geneva talks on intermediate-range missiles.

Both said they felt Moscow still was interested in the type of informal compromise worked out last July at Geneva during the "walk in the woods" by the top U.S. and Soviet negotiators. Simes said he believed the Soviets officially rejected that deal only after they learned privately that Washington found it unacceptable.

Hyland predicted that when West German Chancellor Helmut Kohl visits Moscow next month, he will be presented with a new Soviet proposal that resembles the rejected compromise.

This will be "very tough" for the West to handle because it could have some appeal to Europeans who don't want new U.S. missiles installed, Hyland said.