For months, what some analysts call the "twin towers" -- the huge, stubborn U.S. trade deficit and the federal government's budget deficit -- have cast a shadow over the nation's financial markets.

The shadow fell first on the bond market last spring. Since late March, the value of some long-termU.S. government bonds has dropped by about 30 percent, while those of municipal and corporate bonds have fallen by smaller but still substantial amounts.

In the past two months, culminating in yesterday's virtual collapse, the high-flying stock market felt the weight of the shadow, too. At the market's close yesterday, the Dow Jones industrial average was down 36 percent from its peak in August.

To many financial market participants, the existence of the towering deficits underscore the fact that the federal government, and the nation as a whole, are living beyond their means, with both borrowing heavily to make up the difference between what they spend and what they take in.

As a result of the borrowing, interest rates are higher than they otherwise would be. Since part of the money must come from other countries to finance the international deficit -- estimated at about $160 billion this year -- borrowers in the United States must compete with borrowers around the world. Thus, if interest rates are rising in West Germany, as they have been recently, rates might rise in the United States as well.

All this is greatly complicated by the need for foreign investors in the United States to exchange their currency for dollars to make investments, and to reconvert those dollars when profits are taken home later. When the difference between the level of interest rates in the other industrial nations and the United States changes, it can often affect the value of the respective countries' currencies relative to the dollar.

But recently the governments of the United States, Japan, West Germany, Britain, France, Italy and Canada -- known as the Group of Seven, or G-7 -- have sought to keep exchange rates relatively stable. Under these circumstances, a rise in interest rates in West Germany, for instance, is more likely to be felt quickly here. All of the impact of higher rates there shows up in higher rates here, rather than having part of it absorbed by a decline in the dollar.

Thus, with the twin deficits towering over them, many financial market analysts fear any and all of the apparent alternative outcomes.

If the trade deficit is ever to come down, the dollar's value will have to fall. However, that could mean considerably more inflation as the cost of imported goods goes up. Higher inflation would probably mean higher interest rates.

Alternatively, if the dollar does not come down and the trade deficit stays high, the United States might avoid the inflationary consequences of a falling dollar. But the nation would then have to borrow more money abroad to cover its steadily growing net international debt. And that could mean higher interest rates, too.

Meanwhile, the financial analysts watching the politicized contest between President Reagan and congressional Democrats over taxes and spending remain skeptical that the budget deficit, which fell by about $70 billion in fiscal 1987, will continue to come down.

If it does not, and there is no change in America's low saving rate, the deficit will remain a force pushing interest rates upward.

In other words, there is a strong fear in the markets that the twin towers are going to mean higher and higher interest rates and/or inflation.

Higher interest rates directly mean lower bond prices, because when bond yields go up, bond prices go down.

The impact of these fears on the stock market is much more complex. First, if rates go high enough, it could produce a recession in the United States and much of the world as well.

Recessions can clobber corporate profits, and the value of corporate stocks. Second, higher bond yields can be an attractive alternative to an investment in stocks.

But who wants to make any long-term investment when the prospects for that investment are as uncertain as they are today.

The real problem, to many analysts, is that no one appears to be in charge any more. No one seems to be willing to take the steps necessary to deal decisively with the deficits.

Ironically, the fact that the economy is in pretty good shape -- output is growing steadily and in a more balanced way than at any time in the past three years, and inflation has settled down after higher numbers earlier this year -- only exacerbates fears of higher interest rates and, ultimately, more inflation.

For one thing, the unemployment rate is below 6 percent and more forecasters expect wage increases to be larger next year.

In other words, fear of the future, generated by the existence of the twin deficits and the unwillingness or inability of government to deal with them, has taken its toll.

The recent conflict between the United States and West Germany over coordination of their economic policies has made matters worse by highlighting the current international financial problems facing the United States and the vulnerability of markets here to political and economic developments in other nations.