Kremlin-watching, the arcane offshoot of tea leaf reading that preoccupies most foreigners here but never Soviets, has entered a new period of intense, if frustrating, activity.

With the world's capitals deeply apprehensive about Soviet intentions in the aftermath of the Afghanistan invasion, and the ruling Politburo coincidentally on partial public display because of a local election campaign, Western analysts are looking for any signs of interior leadership strains or intentions.

They are paying close attention to the speaking schedule for the 14 voting Plitburo members for indications of possible shifts in relative standing and are searching their speeches for nuances that could help the West divine future Soviet moves.

Possibly the most important appearance after that of Soviet President Leonid Brezhnev next Friday, will be the scheduled speech Thursday of Premier Alexei Kosygin, who has been absent from public view for four months since reportedly suffering a serious heart attack in mid-October.

Analysts will be looking for evidence of his recovery and stamina for clues to whether the Brezhnev leadership, whose average age is about 70, will be forced soon to make fundamental changes in its composition at a time of world anger and concern caused by the Afghan intervention.

Kosygin, who will turn 76 the day he is scheduled to speak to some Moscow constituents in a televised address, has apparently played no role in either the invasion sequence or the renewed crackdown on internal dissent that has sent Andrei Sakharov into internal exile and brought more than 45 arrests of other activists.

But as head of the government for more than 15 years, Kosygin's continued presence in the Politburo means the kind of continuity and outward stability that has been so important to the Brezhnev leadership.

Most of Kosygin's duties during his absence were handled by Deputy Premier Nikolai Tikhonov, 74, named to the Politburo only last fall and thought to be a possibly Kosygin successor.

Tikhonov's new importance seems reflected in the fact that he spoke recently just after KGB chief Yuri Andropov, just before Defense Minister Dmitri Ustinov, and much closer in time to Brezhnev's scheduled speech than either Moscow party chief Viktor Grishin or Leningrad party chief Grigor Romanoy, both tough-talking Politburo veterans.

This is the kind of ranking that Kremlinologists assess for clues about the internal shape and stresses of the leadership. Taken by themselves such moments perhaps mean very little. But the analysts, equipped with painstakingly assembled records somewhat like racing forms that track who said what, when, and where, sometimes are able to suggest that major reassessments may be underway within the opaque leadership.

For example, Vladimir Scherbitsky, Ukrainian party chief, spoke eighth from Brezhnev this year, while last year he spoke in 12th position and in ninth place in 1975. This seemingly relative improvement in his standing comes at a time when some foreign sources here were already saying they saw signs that Scherbitsky, 64, a known Brezhenv protege, seemed to be wielding more power within the Kremlin.

In this context, it is being noted here that in the portions of his election speech reported by Pravda, Scherbitsky linked international tensions and the need for internal order. The Soviets have invariably moved to tighten domestic control in times of leadership change or severe East-West strain, and the dissident crackdown is well within that pattern.

For the most part, the leaders have offered strongly worded condemnations of President Carter and the Americans, blaming them for allegedly trying to subvert Marxist Afghanistan and plot possible war in the Middle East and Persian Gulf areas.

At the same time, both Andropov and Grishia have told the voters in their districts where they are running unopposed for the Russian Republic Supreme Soviet, or parliament, that a new war is not something to worry about as an immediate threat.

But the analysts are waiting for next weeks group of senior leaders to set an authoritative Kremlin tone, which may include stronger suggestions that the Soviet Union and Western Europe can find grounds for agreement despite U.S. pugnacity. This group includes Foreign Minister Andrei Gromyko, party ideologue Mikhail Suslov, and longtime Brezhnev friend Andrei Kirilenko.

Gromyko has just returned from an unsatisfactory visit to India, where he and the new Indian government failed to reach common understandings on the Afghan invasion.

Suslov last week was in Warsaw, where he called for tighter East bloc discipline and accused the West of repeated attempts to split the Warsaw Pact.

Though his physicians have restricted his working hours, Suslov at 77 has been extremely active in recent months, and is thought to have played a major, although not daily, role in the Afghan crisis.

For the Kremlin watchers, this group offers the remaining hope that there will be fresh clues by the end of the week to the shape of things within the Kremlin.