This city's transit systems are seeking bus drivers, tram drivers and subway clerks. The systems will pay for the new workers' training and make sure they receive good wages and benefits if they qualify. Call now, the billboards urge.

In the Siberian oil boom town of Tyumen, jobs for drillers, welders, pipefitters, and laborers go begging although they offer double and sometimes triple the salaries available in the western Soviet Union.

In Turkmenia, the cotton-rich desert republic along the sensative border with Iran, spinning mills turn at half-capacity for want of trained operators, forcing leaders there to import much of the fabric and clothing the populace needs.

Meanwhile, the military draft may have to be extended from two to three years if there are not enough draft-age youths in the 1980s to maintain the Soviet armed forces at their 3.6 million level.

Everywhere in this strained economy, the "help wanted" sign is being hung out as Soviet manpower abruptly dries up. The severe slowdown in population growth, as well as important demographic changes within that trend, have major implications for the Soviet leadership as it charts the future course for this nation's complex, wasteful, and increasingly ill-coordinated economy.

With 262 million people counted in the 1979 census, the Soviet Union is the third most populous nation on earth, behind China and India and ahead of the United States.But data from the clients tells the tale of declining population rates in stark terms.

While the Soviet Union grew by 33 million people between 1959 and 1970, in the last decade it grew by only 20 million. The dominant ethnic Russian population of 120 million in 1970 grew by only 6.5 percent to 137.3 million in 1979.

Meanwhile, the five Moslem population groups of Central Asia -- the Kazakhs, Kirghizis, Tadzhiks, Turkmenis and Uzbeks -- had a combined population of 19.6 million in 1970 but increased their numbers by 32 percent to 25.8 million in 1979.

If this trend continues, the Great Russians, now in the majority with 52.4 percent of the Soviet population, may slide into the minority position by the end of the century. This demographic change would have important political implications for the Kremlin, which includes 11 Great Russians among its 14-member ruling Politburo.

But there are more immediate problems facing the leadership, now hard at work on the comprehensive five-year economic plan covering 1981 to 1985. This plan will, in all likelihood, be the last one to come out of the era of Leonid Brezhnev.

This new plan will have to take into account the steady slide into stagnation of the Soviet economy.

From boom years of the 1960s, when expansion averaged about 8 percent annually, Soviet production dropped in the past decade to about 4 percent. Although capitalist countries, beset by inflation, unemployment, massive trade deficits and currency dislocations, might easily envy such steady growth, the record was disappointing to Moscow and forbode serious short-comings in this decade.

While the Soviets have sacrificed economic growth to achieve parity in strategic weapon strength with the the United States, there is little posibility of a cut in military spending. The military receives about one-fifth of all economic resources in this country, which has a national production less than two-thirds that of the United States. The failure of the United States to ratify the SALT II treaty and the recent successful test flights by the rival Chinese of a rocket that can hit Moscow guarantee that no reductions will be made in the expensive business of amassing missiles and atomic warheads. Persistent tensions with Peking and poor relations with the West after the Afghanistan invasion also rule out a cut in spending for conventional military forces.

The reduced birthrate denies to planners their traditional means of expanding production -- new manpower for new jobs. Communist cadres proudly boast that the Soviet Union guarantees full employment, unlike in capitalist countries where the drive for maximum profit throws willing workers out of their jobs. But the truth of this claim is that millions here are underemployed, mired in backbreaking, unproductive, low-paid work resulting from inadequate mechanization and upside-down economics rules that reward enterprises on the basis of how many workers they employ.

In Byelorussia, for example, one in four "industrial" workers is, in fact, a manual laborer, shoveling, lifting or hauling by hand what tractors and trucks could do in a fraction of the time and effort. Meanwhile, factory managers traditionally keep dozens and sometimes hundreds of idlers on their rosters just to answer seasonal demands for labor on the inefficient collective farms at planting and harvest time.

Pointing to such easily remedied practices, Western economists say that the Soviets are suffering a phony labor shortage. The water of manpower, however, is entrenched in the national psyche and reforms are still in their infancy after years of hesitant experimentation.

There is no assurance that the leadership in the 1980s can rediscover labor resources. The trend has been the other way. In the last 20 years, almost every able-bodied person has been drawn into the Soviet work force, a development that helps explain the low birth rate in the Soviet industrial heartland.

A. V. Bachurin, vice chairman of the powerful State Planning Committee, has pointed out that while 2.8 million workers entered the job pool in 1976, only 1.5 million will do so in 1980.

The Central Asian population explosion means that one of every four of these workers will be from there. But there is no guarantee that the planners can induce these new workers to take the jobs now going unfilled. Unlike the Slavs who rule them, Central Asians show little inclination to emigrate from their large close-knit, agarian families into the European Soviet Union, where 80 percent of the industry is located, or to Siberia, where vast natural resources must be exploited if national growth is to continue.

Soviet demographers such as Viktor Perevedentsev believe that the answer is in establishing new industries in the Central Asian "sunbelt." In an interview, he pointed out the benefits that have flowed from the development of Azerbaijan's petroleum fields on the Caspian Sea. Azerbijan's Moslem, with close ties to the estimated 14 million people who live just over the Soviet border in northwest Iran, have become famous in the Soviet Union for the cosmoplitan ways, industriousness and slackening birthrate.

But such development is a lengthy, costly process. New industrial bases must be set up thousands of miles from the Soviet center and rural people who share neither the same language nor the same way of life as the rest of the country must be made into an urban work force. While the 1979 census indicates that mastery of the Russian language has improved among the Central Asian population, some Western analysts suspect the figures may have been inflated in an effort so conceal problems.

The census figures for Uzbekistan show that in 1970, 1.3 million Uzbekis claimed working knowledge of Russian as a second language. By 1979, that number had jumped to 6.1 million or nearly half the republic's population. Some Western observers insist that this is not radical improvement, and add that it would not be the first time that scientific or sociological data were falsified in pursuit of Soviet political or ideological ends.

Aside from the Central Asian problem, Soviet planners are grappling with the fact that the Soviet population is aging. There were 40 million pensioners in 1979, or 15 percent of the total population -- an increase of 7.5 million from 1970. Under Soviet law, women can retire at age 55 and men at age 60. Except for senior officials in the party, bureaucracy and the scientific and educational establishments, most Soviets go on pension the day they reach retirement age.

The strain on social services, such as health care and homes for the elderly, has expanded at a time when there is already much criticism of social services at all levels. More than 6 million pensioners are listed as holding jobs -- many because they cannot make ends meet on the meager stipends of about $10 a month.

To expand this work force, the party and government eased the pension laws last October by increasing the limit on how much a worker can earn and still draw a pension. The gains from this sector, however, cannot ultimately amount to much. The economic chiefs face the far more difficult task of finding ways to improve both industrial efficiency and worker production in a country where slovenly labor is a way of life for tens of millions.