WHEN AN AMERICAN politician emerges as a national figure it is natural for him to become the subject of one or more biographies. Any western political leader is interested in maximum publicity. But in the Soviet Union things are done differently. Every Soviet leader is an enigmatic figure -- not just for observers abroad, but also for the citizens of his own country. Even the most prominent officials, including members of the Politburo, often get only a short biographical note in the Soviet encyclopedia or in the "Party Activist's Handbook."

Vladimir Ilyich Lenin, the first Soviet leader, said that when the party selects new leaders, the important points of a candidate's past career should be crystal clear to all party members. The membership should be familiar "with (the candidates') individual characteristics, their strong and weak points, their victories and defeats" (Vol. 8, p. 96 of Lenin's collected works).

Those wishes have long been forgotten. We do not know the individual characteristics of our leaders, their weak and strong points, or even their marital status. This anonymity conceals both their shortcomings and the virtues. The mystery surrounding our leaders is an important reason for the mutual lack of East-West understanding which has grown to dangerous proportions.

But if little is known about many of our leaders, curiosity runs high, especially now, when it is assumed that the top leadership will change by the end of this decade, putting younger men in charge of the country. One of the more interesting younger members of the leadership is little known in the West, which prompts me to put down what little I know about Geidar Aliev.

Prior to 1969, little was known about Aliev even in his native Azerbaijan, though he headed the Azerbaijan Committee for State Security (KGB).

His anonymity in that job was understandable -- the secret police of all countries try to avoid publicity.

Aliev began working for the security organs at the age of 18. I have heard that both during and after World War II, Aliev successfully carried out difficult assignments abroad, in Iranian Azerbaijan and Turkey, and that he knows Arabic, Turkish and Persian. After graduating from Baku University's history department and KGB schools, he began work in Baku in 1950.

We're not likely to learn much about Aliev's assignments in the security organs, but we do know that in the '40s and '50s a regular KGB officer got more than professional training. He had to constantly train his intellect and memory, his physical capacities and his will. It can be assumed that Aliev's career went well. At 42 he became the vice chairman and at 44 the chairman of the Azerbaijan KGB. He was awarded the rank of major general.

That was a time of big changes in the KGB. Aliev, whose talents had already been noticed, could count on a swift rise in the system of "organs," now headed by Yuri Andropov, whose first deputy was Aliev's former boss, Gen. Semyon K. Tsvigun. But Aliev had different plans. He wanted to move from the KGB into the Communist Party bureaucracy. His republic was in disastrous shape, and Aliev knew better than others the scale and causes of this crisis.

Azerbaijan is a relatively small republic in the Transcaucasus. In 1969, its population was about 5 million, mainly Azerbaijanis, a Moslem people. Oil had made the republic an important industrial center even before the 1917 revolution, and after the revolution, many machine- building and chemical industries were developed there. But oil production became more and more costly and difficult, and in other economic sectors, Azerbaijan did poorly. Its industrial growth was slower than other Soviet republics, and its agriculture was less productive. In the 1960s, Azerbaijan was in last place in the U.S.S.R. in growth rates of industry and agriculture.

The majority of Azerbaijanis lived quite poorly. Corruption and thievery reached huge proportions, flourishing almost openly. One of the many commissions sent from Moscow to investigate was astounded. When it made 100 test purchases of various goods in Baku shops, the commission members were cheated, in one way or another, in all 100 cases!

It was plain to all that the republic's leadership had to be changed. The existing corrupt governing apparatus was unable to govern. But who should be the new head of the Azerbaijani Communist Party's central committee? Aliev was a suitable figure, but was virtually unknown either in Baku or in Moscow.

Naturally, friends in important places helped Aliev get the job. Tsvigun, Andropov's deputy at the KGB, was not only a good friend of Aliev's but also a close associate and a relative by marriage of Brezhnev; their wives were sisters. It was Tsvigun who advised that the energetic, intelligent and relatively young Aliev be put in charge of Azerbaijan. On Moscow's recommendation, Aliev was elected party leader of the republic in 1969, and a year later he was the talk not only of the whole Transcaucasus but of Moscow as well.

Aliev moved forcefully and creatively against corruption. Taking advantage of the fact that few people knew him by sight, he would go into shops and restaurants as an ordinary customer, striking up conversations with people waiting in lines and on the street.

On one occasion Aliev pretended to be a farmer driving a truckload of tomatoes to market in one of the Russian cities to the north. Collective farmers in the southern republics were prohibited from sending fruit and vegetables for sale at high prices in the north until they had met their quotas for deliveries to state stores, but these rules were regularly violated. When Aliev himself took the wheel of a truck loaded with early tomatoes, he was stopped at a routine checkpoint, and failed to produce the required documents. But a 25-ruble bribe allowed him to proceed. A KGB car following Aliev's truck picked up the police bribe-taker.

Helicopters went on photography missions to find the luxury dachas of high local officials and black-market moguls around Baku. A campaign began against the practice of buying admissions to institutions of higher learning.

Of course, corruption didn't end in Azerbaijan; it just became more concealed and subtle. And the scale declined noticeably. The Baku press printed sharp and frank criticism of official corruption, and the Baku movie studio made several detective films on the anticorruption campaign. One of them, "The Interrogation," was shown throughout the Soviet Union and received a state prize. His fight against corruption brought Aliev renown. He had many supporters in the republic, but he also made enemies.

Aliev's principal accomplishment was to improve the republic's economic performance. He worked seven days a week, 12 to 15 hours a day. He seemed to carry in his mind all the statistics on the state of Azerbaijan. In dealing with many ministers exposed for corrupt dealings, Aliev didn't put them on trial but showed them the documents proving their guilt, then gave them a warning -- and permitted them to stay at their jobs. After these confrontations, many of these people worked better than newly appointed officials.

In the 1970s, Azerbaijan made a leap forward unusual even for our country. The republic's rates of industrial output went from last to first place in the Soviet Union. Virtually all the economic indices were higher than those for the whole country. In the 1970s, Azerbaijan raised both its agricultural and industrial output by 120 percent.

In 12 years, Aliev had shown his capabilities as a leader. He deserved not only the title of Hero of Socialist Labor that was conferred upon him, but also further advancement. But there wasn't any place for him in Moscow yet.

The corruption that had declined in the Caucasus was growing rapidly in Moscow, and many of Aliev's Moscow friends and patrons were involved. They didn't want to follow his example, and readily accepted expensive gifts. Any politician in our country, even a relatively honest one, must make compromises agonizing to his conscience if he wants to go higher or just hang onto his position.

Contrary to the opinion that developed in the West, Aliev in 1982 was not an ally of Andropov, who was already on his way to power. The sudden suicide of Tsvigun in mysterious circumstances and Brezhnev's serious illness lessened Aliev's chances for advancement.

When Brezhnev made a partial recovery, Aliev persuaded him to come to Baku to award Azerbaijan the Order of Lenin for its successes. This must have been a very important moment for Aliev. He arranged a true king's welcome for Brezhnev, showering him with gifts and attention. Never in his 18 years in power had Brezhnev been received with such pomp inside his own country. Aliev had a good feel for his superior's weaknesses.

Just then, in September 1982, the man widely expected to succeed Brezhnev, Andrei Kirilenko, suddenly resigned from the Politburo, an unexpected end to his political career. On Brezhnev's motion, Aliev was chosen to fill Kirilenko's place. Before his selection could be formally ratified, Brezhnev died. But the new leader, Andropov, could not overturn decisions that had already been taken. Andropov may not have had a great liking for Aliev, but he had to give him his promotion. At the end of November, 1982, Geidar Aliev became a member of the Politburo, the decisive step forward in his political career.

Evidently, Brezhnev had expected to make Aliev one of the central committee's secretaries, an extremely powerful position in the party apparatus. But Andropov suggested that Aliev be appointed a first vice chairman of the U.S.S.R. Council of Ministers, or deputy premier. Andropov gave Aliev the assignment of improving the country's transportation system, which was in serious difficulty.

Aliev went to work with great energy. For him the main thing was not to make mistakes. Soon he was given responsibility as well for culture, education and public health. When production plans for consumer goods were unfulfilled and all the ministries -- even the Ministry of Defense Industry -- were given targets for consumer-goods production, Aliev headed the inter-agency commission for consumer-goods production.

Soon Aliev began to receive not only economic but also foreign-policy assignments. He headed a Soviet delegation to Vietnam. A few months later he flew to Syria to familiarize himself with the situation in that hot spot.

The rise of Geidar Aliev aroused alarm in certain circles because of prejudice.

There is much anti-Moslem sentiment in the Soviet Union.

One nationalistic Russian intellectual in Moscow has assured me that Aliev will help ruin the Russian north. Not so long ago, a Russian intellectual who lives in the Caucasus said to me: "Don't you fear the coming to power of Moslems in the U.S.S.R.?"

"No, I don't," I replied. "Aliev is an Azerbaijani and a communist and not a Moslem," I said.

"Oh," he answered, "for us in the Caucasus it's all very different from what you imagine in Moscow. Once a Moslem, always a Moslem."

No doubt Aliev is aware of the difficulties of his situation as a son of the Caucasus and Azerbaijan. He works hard, presumably realizing that his energy and talents will be needed in Moscow, where too many leaders have passed the age of 70 or 75.

Aliev hasn't brought friends and relations from his home base in Baku to join him in Moscow the way, to cite one example, Brezhnev did. He makes friends in Moscow. He has frequent meetings with the most diverse people and almost always they come away with the best of impressions. He has frequently spoken out: on school reform at the Supreme Soviet session, on problems of the cinema at a movie-makers' conference, on public-health problems at conferences of medical professionals. His accentless Russian is better than many Russian leaders'. His popularity in Moscow has undoubtedly grown. Aliev often meets foreign diplomats. Several years ago a group of ambassadors from various countries went on an excursion to Azerbaijan. Aliev received them in Baku. He didn't evade sharp questions when, in particular, they came from the Italian ambassador. Recently, Aliev attended a reception at a Latin American embassy in Moscow. The Italian ambassador went up to him and asked, "Do you remember me, Mr. Aliev?"

"And do you remember me, Mr. Giovanni Migliuolo?" Aliev replied. Maybe Aliev knew ahead of time who would be at the reception, or maybe his phenomenal memory helped him. Migliuolo, Italy's envoy to Moscow since 1981, was flattered.

Kirilenko, whose place in the Politburo Aliev took, used to forget even the names of his closest associates and sometimes confused the names of foreign guests. His interpreter would have to correct these lapses by a man who for a long time was considered Brezhnev's most likely successor.

People who know Aliev well tell me that even now his prospects are underrated. Personally I don't think that Aliev will be the choice if the party needs to appoint a new general secretary of the central committee in the foreseeable future. But when the time comes for the departure of the aging premier, Nikolai Tikhonov, Aliev might well get the job.