The reported hospitalization of Soviet President Leonid Brezhnev has intensified rumors and speculation that the Brezhnev era may be drawing to a close and that the power struggle for his succession has begun.

Brezhnev, 75, has been ill before, each time setting off speculation about the succession, but each time he has managed to recuperate and emerge even more firmly in control of the Kremlin. There are no visible indications this time that his power is being challenged directly.

The Associated Press, quoting a reliable Soviet source, reported Sunday that Brezhnev had returned home and was recuperating slowly from an undisclosed ailment. The source said Brezhnev, who may have suffered a stroke, is under constant medical supervision and could be rehospitalized at any time.

Semiofficial Soviet sources who frequently pass information to Westerners suggested yesterday that a picture of Brezhnev was likely to appear in the Soviet media as soon as he recovers sufficiently. No photographs of Brezhnev have been published in the past eight days, and there have been no public suggestions that he was incapacitated.

Nonetheless, rumors have mushroomed about Brezhnev's condition and the jockeying for position by the Kremlin's senior politicians. While the hospitalization is the immediate reason for this, other crucial questions are pressing the Kremlin's aging leaders, including the problems of the Soviet Union's stagnating economy and sensitive foreign policy and security matters.

Kremlin policies these days are a product of entrenched interests that are more durable than any single personality. Brezhnev's success as leader has hinged on his skills as manager of the ruling Politburo and as a careful broker.

While securing continuity and stability, the years of consensus government have postponed many acute problems that now appear to have come to a head. From their walled-off Kremlin offices, the leaders see danger in all directions.

Although it is the world's largest producer of oil, the Soviet Union has begun to feel the energy squeeze. This in turn has exposed structural weaknesses in the Soviet economy that will have to be cured soon if the country is to avoid a serious crisis. Industrial inefficiencies and corruption, once concealed, now are subjected to public scrutiny. Agriculture has become an annual disaster for the past three years, and huge amounts of hard currency are required to buy food abroad.

In foreign affairs, detente is in deep trouble. Poland and Afghanistan have proved to be far more costly ventures than originally anticipated. Moscow's aid to its far-flung clients has imposed other economic strains. Above all, the United States not only has repudiated the latest agreement on strategic arms limitations but the Reagan administration also is seen here as having embarked on a massive rearmament program to achieve military superiority.

Even before Brezhnev's most recent illness, rumors of a power struggle dominated conversation here. They began with the death in January of Mikhail Suslov, a senior party figure and key Kremlin player for nearly three decades, whom many here considered the real power behind the throne.

Suslov's death was particularly significant because, as the guardian of Marxist orthodoxy, he held a pivotal position in the Communist Party.

Other Politburo figures whose deaths or political demise weakened the party included the late premier, Alexei Kosygin, former president Nikolai Podgorny and the former deputy premiers Kiril Mazurov and Dmitri Polyanski.

With its 18 million members, the party is still an elite among the population of more than 262 million. But its glamor has faded and its ideological edge has been blunted.

Two institutions with powerful influence in any reshuffle are the armed forces and the KGB security police. The Army is represented on the Politburo by Defense Minister Dmitri Ustinov, while the KGB's representative is Yuri Andropov.

The prevailing view is that the armed forces' role could be decisive, particularly because changes are likely to take place at a time when the Kremlin sees itself confronted by an implacably hostile and reckless administration in Washington.

The armed forces have been pampered by Brezhnev. But there are indications that the military has been demanding more resources to meet the American challenge even as he pressed for cuts in the burdensome military budget.

In this context, it is believed here that the senior commanders led by Marshal Nikolai Ogarkov, the chief of staff, would expect any new leader to give the armed forces a greater share of the pie in the already fierce competition for money, manpower and resources.

The KGB, whose power has been kept in check by Brezhnev, was expected to seek greater freedom to deal with perceived internal threats, ranging from corruption and Western influences to rampant consumerism and ideological apathy.

Like the armed forces, the KGB may gain greater authority at a time when the Americans are perceived here as waging a massive campaign to undermine the socialist system. Ironically, KGB chief Andropov has been persistently rumored to be a man of modern, liberal outlook.

While their influence is great, neither the armed forces nor the KGB are expected to provide the new leaders. These are most likely to come from that sector of the party elite most closely linked to the control of the economy, and especially of heavy industry.

The lines here seem to mesh and involve regional interests as well as those of the armed forces. Andrei Kirilenko, apart from Brezhnev the only man to serve in the Politburo for more than 20 years, has been the party's top official for economic and industrial policy.

But since Suslov's death, Kirilenko, 76, has made infrequent appearances at public functions and has been upstaged by Konstantin Chernenko, 70, Brezhnev's protege and longtime chief of staff who joined the Politburo less than four years ago. The Chernenko-Kirilenko rivalry has been the talk of the town for the past two months.

Just what goes on in the minds of the 30 or so key figures at the peak of Kremlin authority is a mystery. There have been no rumors of younger men aspiring to the top positions.

Apart from Brezhnev, only Kirilenko and Chernenko hold seats in both the Politburo and Secretariat. In the Soviet decision-making process, all issues are first dealt with by the 11-member Secretariat of the party's Central Committee before being put to a vote by the Politburo.

At the moment, Chernenko is reliably reported to be coordinating Secretariat activities, the job once held by Kirilenko. Chernenko is also said to be sitting in for Brezhnev at Politburo sessions. However, this is an informal arrangement due to his close association with Brezhnev.

Chernenko is also said to have taken the job once held by Suslov, but that has not been confirmed formally yet.

There was speculation that Brezhnev's recent heavy schedule, which included two major foreign policy initiatives, had been designed to show him as vigorous. He was to have addressed a Central Committee plenum and to push for personnel changes such as Chernenko's confirmation as Suslov's successor. The plenum, however, has been postponed because of Brezhnev's illness.

According to this line of thinking, the succession struggle at the moment remains wide open.