The order was firm and to the point: Cease flying. The Department of Transportation issued it earlier this month to Discovery Airways, a small company operating flights between the islands of Hawaii. The department's concern was not safety. Rather, Discovery had been ruled to be under the financial control of foreigners, in its case Japanese and Italian, violating a little-known law that requires that domestic airlines be owned by Americans.

The U.S. economy is one of the world's most open. Foreign companies have sunk more than $400 billion of direct investment into myriad industries coast to coast, ranging from fast food to banking to high technology. Yet buried in federal statutes are laws like the one applied to Discovery that grant or withhold privileges to companies based on the nationality of their owners.

Now, influential people in Congress, industry and parts of the federal bureaucracy are pushing hard to expand that philosophy. They are fighting an uphill battle against the Bush administration, state governments and foreign investors themselves. But they argue that controls of some kind are crucial to preserve the nation's competitiveness at a time when many American companies are being overrun helter-skelter on their home turf by rivals from abroad. Foreign countries regulate investment, they say. So should we.

Through sales of U.S. companies, said Rep. Doug Walgren (D-Pa.), "we transfer to foreign purchasers the economic advantage America will need in the future."

About 15 bills that would treat foreign companies as different from American ones are pending in Congress. Elsewhere in Washington, questions like these are being debated:

Are foreign-owned companies paying their fair share of taxes?

Should they still be allowed to set up political action committees?

Should they be able to buy high-tech firms?

"It's open season on foreign investors," lamented Brad Larschan, counsel to the Association for International Investment, a Washington group that represents many foreign companies with holdings here and is fighting the trend.

The new concern, suggested Prof. D. Jeffrey Lenn of George Washington University, "is symptomatic of a larger economic and political shift that's taken place." It reflects "a new awareness of the fact that the U.S. is a debtor nation."

Since the early 1980s, the nation has been hemorrhaging dollars to the outside world through trade deficits and is now witnessing a wave of foreign investment as billions of those dollars come back as capital.

With debates like these, the United States is inching toward coming to terms with a key issue of economic life in today's world:

Does the future lie in openness, in the creation of a single global economy? Or will national borders remain an important and legitimate means by which countries maintain their own standard of living and technological advancement and insulate themselves against unfair trading practices from abroad?

For all the emphasis on the flow of funds into the United States, talk of reining in investment comes at a time when U.S. companies are continuing to invest heavily abroad. Even if many of the proposed laws are never enacted, the debate itself could have an impact.

Of particular interest to many American companies is buying into Europe in advance of the scheduled 1992 economic integration. A closing of the doors here could lead to retaliation by foreign governments that would argue it was a violation of "reciprocity," the notion that access for investment should be generally the same from country to country.

Jokes that the United States is being "bought out" by foreigners, particularly Japanese, nevertheless, are becoming a staple in TV and popular culture. But at a policy-making level, those who advocate restrictions are by no means in the majority.

Many Americans at the state or local level view foreign capital as a crucial job creator. The Bush administration has put itself firmly against measures it feels would restrict the United States's traditional welcome to foreign capital. It has moved only once to block a foreign deal under a law allowing such action on national security grounds, ordering a Chinese company to sell a Washington state aerospace contractor it had bought. The order against Discovery Airways came out of Department of Transportation enforcement of another law.

The critics generally hold high the banner of national interest. But other forces are at work, too.

On Capitol Hill, the investment issue is highly partisan, pushed by Democrats against a Republican administration. In the industrial world, it can be used to restrain competition or to head off hostile takeovers.

Perhaps the oldest front of the Washington battle over foreign investment is statistics. Currently, many federal agencies gather data, but critics say the results, published in a form that cloaks specific companies and deals, are vague and may vastly understate the true levels. While better statistics is the purported goal, many of the supporters have already made up their minds that there is too much.

Various bills have been introduced that would require foreign companies to disclose more data about their operations or make data that is already collected available to more agencies, such as the General Accounting Office.

After insisting for years that the system did not need fixing, the White House now says change is in order. It is backing a competing bill that would allow the Commerce Department and Census Bureau to share confidential data they already collect. But it would not allow it to go to other federal agencies, arguing that if spread too widely information will leak and discourage companies from providing accurate data in the future.

The battle goes far beyond statistics, however.

In June, the House passed a bill sponsored by Rep. Jack Brooks (D-Tex.) that would make it easier for companies to organize joint production ventures, a step that Brooks argues would help them compete against similar tactics abroad. The bill specifies, however, that the legal relief would be denied to any consortium that had more than 30 percent foreign ownership. In addition, the production would have to take place within the border of the United States to qualify.

Another House bill, offered by Rep. Edward J. Markey (D-Mass.) for the general regulation of the cable TV industry, would limit foreign ownership of cable systems. Federal law for decades has limited foreign ownership of TV and radio broadcasting, on the grounds that (like airlines) they could be vital assets in wartime; the cable bill, its supporters say, would merely extend that principle to an industry that is coming to rival the older two as a distributor of information.

Still other legislation, backed by House Majority Leader Richard Gephardt (D-Mo.), would place new tax-reporting requirements on foreign-owned companies in this country. This is being pushed at a time when the Internal Revenue Service is auditing the books of many foreign companies doing business here and concluding that some have manipulated their accounts to downplay profits and avoid paying U.S. taxes.

Elsewhere in Washington, the Federal Elections Commission is debating whether it should continue to allow the U.S. subsidiaries of foreign companies to set up political action committees. Pillsbury, for instance, long an American corporate icon, is now British-owned and under the change would not be able to sponsor a PAC.

Almost all the measures in the end get to the notion of "national treatment," a legal concept that has governed the U.S. approach to foreign companies for decades. Generally, it holds that in the United States a foreign-owned company will receive rights and privileges not less than those of American-owned companies.

There are many exceptions, but the principle is that the foreign company should be taxed at the same rate, be able to enter the same businesses and have the same rights to organize its American employees as a political action committee (although, like American-owned companies, it cannot directly fund the PAC or make direct contributions to campaigns).

National treatment is a core concept in international law, embodied in many treaties and agreements. But like many others, such as free trade, it is more reality in some countries than others. Critics of current U.S. investment policy point out that Japan and many of the Western European countries, not to mention developing countries, continue to regulate foreign investment closely, approving or rejecting individual projects based on whether they fit into national economic objectives.

It is not in the U.S. economic interest to allow foreigners to buy out small U.S. venture firms that are developing next-generation technology, the critics often argue. Behind the scenes, lobbyists and concerned officials have sought to block friendly takeovers of U.S. firms by Japanese buyers, such as the proposed purchase of Semi-Gas Systems, a small Silicon Valley firm that makes semiconductor production equipment, by a Japanese company.

A bill sponsored by Walgren would, among other things, require the inter-agency Committee on Foreign Investment in the U.S., which reviews takeovers that are deemed to have national security implications, to investigate any foreign takeover of a company involved in technologies declared to be "essential."

The White House continues to fight the trend. It maintains that the free movement of capital across national borders is essential to prosperity. What matters is not who owns a company but whether it keeps jobs and technology in the United States.

Cheering it on is Elliott Richardson, who lobbies for foreign companies in Washington and argues that critics of investment have their priorities wrong. A big capital influx is inevitable, he says, as long as the United States continues to run major deficits in trade and government financing.

"If you're worried about foreign investment," he told a group of skeptical legislators at House hearing recently, "you ought to be dealing with it through the fiscal and trade deficits. There's no other way to do it."