It is said that it was one of the most eloquent speeches Andrei Gromyko ever made, without notes, speaking to members of the Soviet Communist Party Central Committee last Monday and telling them why they should elect Mikhail Gorbachev as the new Soviet leader.

The veteran foreign minister praised his younger Politburo colleague, his qualities and his political experience.

"Comrades," Gromyko said, "this man has a nice smile, but he's got iron teeth."

It was the vote of confidence nobody in the room could match -- from a man who sat at Stalin's elbow in Yalta and Potsdam, and who was a key adviser to all subsequent Kremlin chiefs and has come to symbolize, at least in the party's eyes, the last visible link of continuity for more than 40 years of history.

After Gromyko ended his speech, Politburo member Dinmukhamed Kunaev asked for the floor. Kunaev, a crony of the late Leonid Brezhnev, has come to be regarded by younger generations here as merely another intransigent member of the conservative old guard. He was deputy premier of Kazakhstan when Gorbachev was 11 years old.

"You should not think I am saying this because I'm speaking second, but I want to tell you that the 800,000 Communists of Kazakhstan want this man," he said, looking at Gorbachev, according to an authoritative account.

Generational change, after two quick Kremlin transitions and the paralysis of Brezhnev's last year in power, was formalized Monday afternoon when Gorbachev was elected general secretary of the Soviet Communist Party.

The actual selection of Gorbachev for the post was made Sunday night, three hours after the death of Konstantin Chernenko. Again Gromyko, speaking first at a meeting of the top leaders, immediately proposed Gorbachev to be chairman of the funeral commission. The proposal was endorsed.

Only Moscow-based members of the Politburo, alternate members and secretaries of the Central Committee were at that meeting.

But the transfer of power was so smooth and quick as to indicate that Gorbachev as heir apparent had been agreed upon long ago to move into the top slot once Chernenko left the political stage.

Indeed, all three power transitions during the past 2 1/2 years seemed to have been based on relatively coherent and consistent processes, in contrast with the Kremlin intrigues and power struggles that marked past leadership changes.

In the last months of Brezhnev's life, when distinct factions were clearly jockeying for positions, it was said that the ruling elite had come to believe that it was mandatory to devise a mechanism for orderly succession.

By all indications, the current system was established during the course of struggle between Chernenko and the late Yuri Andropov in the fall of 1982. Chernenko, a Brezhnev protege, was defeated in the struggle, but he was given the post of party secretary in charge of ideology, the second position in the party hierarchy.

Andropov held the second slot at the time of Brezhnev's death and was elected to succeed him. When Andropov died in February 1984, Chernenko moved from the second slot to become leader while Gorbachev, an Andropov protege, was given the second slot. When Chernenko died, Gorbachev moved to the top slot, but it is not clear yet who will be party secretary in charge of ideology.

There was speculation here that the job would go to Viktor Grishin, 70, the party boss of Moscow and a member of the old guard.

All that can be said about the latest transfer of power here is that the system has demonstrated more maturity, resilience and flexibility than many thought it had.

It is too early to expect any specific indication of the kind of policies Gorbachev intends to pursue and the sort of coalition he intends to build. But his interests seem to focus primarily on domestic issues, and he clearly signaled that he intended to continue Andropov's program for sweeping economic changes.

Andropov planned to introduce initiatives that would introduce a measure of decentralization into the Soviet economy, such as offering incentives to managers for improved production.

At a rally in December, Gorbachev made a speech that seems to echo Andropov's program, which is likely to become his own now:

"We will have to carry out a profound transformation in the economy and the entire system of social relations," Gorbachev said. "The process of the intensification of the economy must be given truly nationwide character, the same political resonance that the country's industrialization once had."

The only specific reference Gorbachev made in his acceptance speech Monday involved the November 1982 Central Committee plenum. It was at this plenum that Andropov was elected Soviet leader and that he made clear that he wanted to revitalize Soviet economic and social life.

Analysts here believe that Gorbachev has inherited Andropov's political base, which comprised the military establishment, the KGB secret police that Andropov headed for 15 years and the younger and better educated party cadres.

Equally if not more important, however, is the fact that Gorbachev has assumed power at a fortuitous time. The country has been dispirited by the frequent changes in the Kremlin and the specter of old men ailing and unable to assert themselves.

Thus, Gorbachev's youth, the absence of personal links to the excesses of the Stalinist period, his speechmaking ability and personal style all have combined to give him a degree of instant public acceptance that few Soviet leaders ever have enjoyed.

"He has a chance," as one Soviet observer put it, "to start with a clean slate." A series of vacancies at the top and the scheduled party congress later this year will provide Gorbachev with the opportunity to bring fresh blood into the Politburo and the Central Committee.

On the other hand, he will have to contend with the old guard, which still holds several of the most important positions in the party and government, and he will have to deal with the vast party bureaucracy and its proverbial inefficiency.

It is the party bureaucracy that had made the system, particularly the economic system, resistant to changes in the past.

What Gorbachev's intentions are and how he plans to run the party and the country is still a mystery. His first priority apparently is to gain control over the huge apparatus of power, because changes in the Soviet Union can be imposed only from the top and by a leader who controls all levers of authority.

It will take some months -- if not more -- for Gorbachev to consolidate his authority. So far, he has managed to impress various foreign leaders who met him here during Chernenko's funeral. It may be more difficult to impress regional party chiefs and their teams and enlist their support for his plans to revive the economy.