A subtle shift in personnel in the top layers of the immense Soviet bureaucracy has recently precipitated a flurry of speculation among Western analysts about who might succeed Soviet President Leonid Brezhnev. This shuffle has been brought about by the death of a key Brezhnev lieutenant, the illness of two key Soviet leaders, and the unexpected promotion of one Yuri Andropov. It has offered intriguing new clues to ''Kremlinologists'' - scholars of developments in Moscow's Kremlin compound of government - as to how the coming Soviet succession may unfold.
Few Americans noticed these changes in the upper echelons of the Soviet government. Fewer still may have grasped the significance a new generation of Soviet leadership may have for the future of East-West relations.
But from these changes the question arises: What does it matter to the average American how the Soviet succession struggle proceeds?
I studied the intricacies of Soviet leadership politics last summer as I prepared for wide-ranging talks which a Senate Foreign Relations Committee colleague, Charles ''Mac'' Mathias of Maryland, and I held with West European and Soviet leaders. And I have since undertaken extensive research into what is known about the Soviet succession struggle and the functioning of the Soviet leadership.
Kremlinologists know remarkably little about the ruling Soviet Politburo and its adjunct, the Secretariat of the Soviet Communist Party. The policy-oriented Politburo is probably the world's single most powerful decisionmaking body, while the Secretariat provides a springboard to leadership through its control over Soviet personnel decisions. In these two bodies, decisions are made in deep secrecy which have a profound effect not only on the lives of the 250 million citizens of the Soviet Union but on the lives of all Americans and other peoples of the world.
The American cabinet, less powerful as an operative body than the Politburo, works with a good deal of transparency because of our open society, our enterprising free press, and numerous contemporary memoirs. In striking contrast , the Politburo and the Party Secretariat operate in almost total darkness. Western experts must piece together the slightest signs of changes in the Soviets' ruling line-up to decipher what might be going on behind the scenes and , in turn, what we might expect from new Soviet leadership.
Kremlinologists pore over photos from official Soviet celebrations to see who may have moved up in rank. Applause given senior Soviet officials at public functions is measured as one possible indication of who is gaining favor and who is ''on the outs.'' Of course, there are other tools available to experts in our government. These include diplomatic exchanges with senior Soviet officials, our intelligence community, and interviews with emigres and defectors.
In recent weeks, Kremlinologists have been studying the changes at the top of the Soviets' ruling structure that could portend new departures for Soviet policy and that offer us some clues as to how the succession battle might unfold.
This process began last January with the passing of Mikhail Suslov, the chief theoretician of the Soviet leadership and, for all purposes, the number two man behind the Brezhnev dictatorship. Suslov's death came during a period of steady deterioration in President Brezhnev's physical condition. Brezhnev was quick to push forward an undistin-guished and nondescript loyalist, Konstantin Chernenko.
Kremlinologists now generally doubt that a single figure will be able to seize the reins alone once Brezhnev finally topples from power.
The most interesting development in the Soviet leadership since Suslov's death has been the promotion of a serious rival to Chernenko. Along with Chernenko and Brezhnev, only Andrei Kirilenko and Mikhal Gorbachev had until recently been members both of the policymaking Politburo and of the personnel-controlling Secretariat. Kirilenko has loomed as a possible rival to Chernenko, but reportedly he is seriously ill. Gorbachev is a generation younger and, as an agricultural expert, has a limited power base. Gor-bachev and Defense Minister Dmitri Ustinov apparently are very dark horses in the succession competition.
But last May 26 a terse announcement was made that the longtime head of the Soviet KGB, Politburo member Yuri Andropov, had been relieved of his intelligence and secret police duties and that he had joined the ten-member Communist Party Secretariat. Andropov's ascendancy, and the naming of Andropov loyalist Vitaly Fedorchuk as his KGB replacement, are signs that Andropov, at 67 , now is a serious contender for leadership in the post-Brezhnev era.
Andropov is viewed by many Kremlinologists as the most intelligent and cerebral of potential Soviet leaders. But too many Western analysts have mistaken his urbane savvy as sympathy for Western values. It is true that Andropov is worldly; he alone among contenders in the Brezhnev succession speaks English and has considerable experience in foreign affairs. His experience could lead to a more effective East-West condominium should he play a central role in the future Soviet leadership. But it could also spell greater trouble for the West. While the post-Brezhnev leadership is not likely to turn its back on the pursuit of superpower arms reductions, a stridently nationalistic and militaristic stance might provide one calculating challenger to the throne with the power base he needs to emerge victorious in any succession struggle.
The fact remains that our knowledge of the internal machinations of the Soviet government is quite limited. And it doesn't take a Kremlinologist to define the immense and obvious problems which will confront the new Soviet leaders.
Regardless of whether it is Chernenko, Andropov, or - more likely - a combination of the two and perhaps others, the new Soviet leadership will be beset by a decaying economy, a failing agricultural system, crises in Poland and Afghanistan and mounting global pressures for US-Soviet arms reductions. And into the hands of the new Soviet leadership will fall the immense responsibility shared with the American president for averting a nuclear confrontation that could end civilization.