Multinational corporations and the Third World countries in which they invest huge sums of money have dropped some of their mutual suspicion and hostility and are learning -- of necessity -- to live together.

That is the main conclusion of a new study written by former State Department official Isaiah Frank and published by the nonprofit Committee for Economic Development and its overseas counterparts.

The study notes that "foreign investment is occasionally denounced on the grounds that it takes out of poor countries more than it puts in." For example, in 1974 -- the latest year for which data are available -- the multinationals repatriated profits of more than $16 million from developing nations but brought them only $7 billionin new capital.

Frank says that a simple comparison of these two flows is not valid for many reasons, including that the profitsrelate to prior years's investments. Moreover, he says that the fundamental question is how the foreign investment has added to output and real income in the host countries.

But the report does not come up with any conclusive way of evaluating the impact of multinational's investments on the economic of the Third World. t

Historically, the big multinational companies and their home governments expected the Third World to accept private capital flows more or less passively, providing a hospitable climate with a minimum of regulation, as well as tax and other economic inducements, the report says.

But the poor countries receiving the multinational investments felt they were involved in "basically an exploitative relationship" that in the long run would trap them in their poverty conditions, while returning rich rewards to the companies and their stockholders.

This feeling has not been eradicated totally in the Third World, says Frank, now a professor at the Johns Hopkins University School of Advanced International Studies.

But he says that the CED study -- based on interviews with 90 multinationals based here, in Europe, in Japan and Australia -- shows that tensions are abating, but further effortis needed to resolve differences.

"Fortunately, the old stereotypes and their modern versions are giving way on both sides to more reasoned and thoughful views of the problems confronting developing countries and of the role of multinational corporations," the report says. "The companies are more sensitive to the fear of developing countries about foreign domination of their economies."

Interestingly enough, one reason for the new ability of multinationals "to empathize with the determination of other countries to control their own destinies" was the object lesson of growing Organization of Petroleum Exporting Countries influence on the rich nations of the world after the 1973 oil price shock.

At the same time, despite political rhetoric to the contrary, many developing countries are more self-confident in their technical negotiations and believe increasingly in their ability to control the multinationals.

According to the study, the total amount of foreign investment in developing countries was more than $85 billion by the end of 1977, a doubling in the decade, reflecting a substantial increase even after allowances is made for inflation and dollar depreciation.

Investment by U.S.-based multinationals declined from 50 percent to 47 percent of the total, while there were dramatic increases in the shares held by Japan (from 2 percent to 6.7 percent) and by Germany (from 3.4 percent to 8 percent).

Most companies long since have given up the notion that their problems in the Third World have much to do with ideology. In fact, some of the most stable and profitable relationshipsare with Socialist bloc in Eastern Europe.

The key deterrent to investing and operating abroad appears to be in instability resulting from "arbitrary and unpredictable alterations in the rules of the game after investment decisions have been made," the report says, and it cites five forces that create themost tension:

Rapid economic growth that gives "increased bargaining power to developing countries."

Alteration of national goals as Third World countries undergo profound social changes.

"The obsolescing bargain," especially in investments in natural resources, that comes into play as "both parties . . . experience altered perceptions of what constitutes a fair deal."

When hard-pressed governments are unable to satisfy the needs and aspirations of their people, multinationals "can serve as convenient scapegoats."

There is a dilemma facing Third World nations as they try to get the best gain out of foreign investment. For example, if multinational repatriate the bulk of their profits, they deprive the host country of much newly created national wealth. But if they reinvest the bulk of the profits, they are further increasing their ownership and control of the local economy.