Off the coast of Malaysia an Exxon rig drills for oil in coastal waters. In Singapore, Texas Instruments operates a multi-million-dollar electronics factory. In Thailand, Chase Manhattan Chairman David Rockefeller is received by the prime minister and king as a matter of course.

U.S.businessmen in Asia today read a local edition of The Wall Street Journal. They check into U.S. chain hotels when traveling. If they need to arrange financing for a venture, they often can find offices of their home-town banks.

Five years ago, the U.S.armed forces disengaged from the Southeast Asian mainland after the Vietnam defeat. But U.S.businessmen by no means followed them. Staying behind, they have seen commercial relations with Southeast Asia rise to heights never envisaged when U.S. firms first reached the region in numbers in the 1960s.

Like their counterparts from Japan and Western Europe, U.S. executives Southeast Asia as a high-growth, low-risk market. Communization in Indochina, fighting in Cambodia -- these have been dismissed as sideshows to the brisk economic expansion under way in other countries in the region.

In the late 1970's, the five members of the Association of Southeast Asian Nations (ASEAN) -- Thailand, Malaysia, Singapore, Indonesia and the Philippines -- consistently reported real growth of between 5 percent and 10 percent, twice the average in the industrailized world.

economists cite oil and other resources, a prosperous farm land and relative political stability to explain this proformance.

Two-way U.S. trade with ASEAN grew almost fourfold between 1973 and 1979 to $16 billion. (U.S. trade with all countries increased less than threefold in dollar terms during this period.) Increasingly, U.S. exports are capital goods to sustain ASEAN's growth.

Dozens of U.S. banks, meanwhile, have opened offices in ASEAN capitals . U.S.investment in the 1970's took off, too. U.S. Embassy reports suggest it tripled between 1970 and 1975 to reach $3.5 billion and has continued to grow since then, though at a far more conservative pace.

Today many ASEAN capitals are ringed by light industrial plants turning out electronics equipment, textiles, automobiles and a host of consumer goods formerly imported. Many factories are joint ventures with foreign investors. "You can always find a Colgate-Palmolive factory within a stone's throw," says a U.S.businessman who travels frequently in the region.

Singapore is the exception among ASEAN's generally agriculturally-based economies. A 235-square-mile island with virtually no resources, save people, it has geared its entire economy toward foreign capital.

Offering telephones that work, honest and efficient bureaucrats (a rare commodity in other ASEAN countries), skilled workers and free repatriation of earnings, Singapore has filled its carefully planned industrial estates with foreign-controlled factories.

The U.S. Embassy there has estimated U.S. investment in fixed assets alone has reached $800 million. The range of manufacturing runs from stereo records to electric irons to aircraft parts. Altogether, something close to 500 U.S. companies now do business in Singapore.

During the 1970s, Singapore also emerged as headquarters for the regional oil industry, in which U.S. firms play the dominant role. Esso has entered a major refinery project. Small Texas-based exploration companies operate boats and helicopters from bases in Singapore.

U.S. firms have worked on two enormous liquification plants in Indonesia needed for the export of natural gas. In Malaysia and the Philippines they operate production platforms and pipelines in extensive offshore oil fields. Two U.S. firms, Union Oil and Texas Pacific, are spearheading a Thai project to tap gas fields in the Gulf of Saim.

With the corporation have come their bankers. "Banks you'd never expect to see overseas have opened offices in Singapore," remarks a financial counsultant. Among them, for instance, are Citizens and Southern National Bank of Georgia and Harris Trust and Savings Bank of Illinois.

Some specialize in financing trade and retail banking. In 1977, for instance, the Singapore branches of Citibank and Bank of America topped all local banks in terms of assets ($2.4 billion for Citibank and $2.2 billion for Bank of America). 1970s, ASEAN countries have borrowed heavily to offset current account deficits and finance development projects -- in 1979 alone, the Philippines sought commercial loans of just less than $1.1 billion.

In the mid-1970s, the large U.S. banks created special merchant banking units -- Chase Manhattan Asia and BA (Bank of America) Asia are among the largest -- to manage and fund the jumbo syndications regional borrowers were starting to take.

Businessmen have assumed the role of informal U.S. envoys in some ASEAN countries. In Singapore, the U.S. ambassador carries little clout -- "diplomats come last in the Singapore hierarchy," says a former embassy official there. But corporative executives, expecially ones with large operations in the republic, have access to the highest levels of government.

Indonesian leaders are forced to give foreign bankers an ear. Morgan Guaranty organized an emergency refinancing package for Pertamina, the state oil company, which in 1975 brought itself and some say the entire Indonesian economy -- close to collapse by squandering hundreds of millions of dollars in loans.

When David Rockefeller tours the region -- he visited all five ASEAN countries earlier this month he sees prime ministers and heads of state. During his 48-hour stay in Thailand, the military flew him to a Cambodian refugee camp, a tour normally reserved for visiting government leaders.

But despite their advances in the past decade, U.S. banks and coporations now face intense competition for the ASEAN market. Japan already has pushed ahead in trade or investment, and the EEC countries also are moving aggressively in loans and manufacturing.

In Thailand, for instance, U.s. vehicle assembly plants closed in the late 1970s. "GM and Ford got kicked out by the Japanese," says a Bangkok businessman. "They were competing head-on with the Japanese and lost."

Still, most economists see little chance that U.S. businessmen will be forced from the scene altogether. Decades-long business ties and continuing dominance of certain key industries -- passenger aircraft, military equipment and computers, to name a few -- will ensure and that ASEAN remains a strong market for the United States for many years to come.