The United States has sharply protested the presence of Cuban troops in Angola. But, ironically, part of those troops' military task is to guard the operations and workers of a major U.S. corporation - Gulf Oil of Pittsburgh.

Behind a protective screen of about 2,000 Cubans, by State Department estimate, Gulf's 125 offshore wells pump 122,000 barrels per day of petroleum to be shipped to the United States, Japan and Europe. While official U.S. aid to Angola is prohibited by act of Congress, the taxes and royalties from Gulf Oil are estimated to provide 60 to 80 percent of the Angolan government's operating revenue.

The Cuban troops are in Angola to make sure the oil, and the revenue, keep flowing. The explicit threat to the pumping operation is a guerrilla force - backed by neighboring Zaire - which calls for the secession of the oil-rich enclave of Cabinda, a legacy of Portuguese colonialism. Another presumed threat arises from Angolan insurgents who contest the rule of the Moscow-backed Luanda regime.

At the international political level bitter rhetoric continues, with no sign that Washington is ready even to grant diplomatic recognition to the Havana and Moscow-backed Luanda regime. But at the business level, calm and compromise have characterized nearly completed negotiations between Angola and Gulf over the terms of a new contract. The Angolan side's consultant in the negotiations is no Marxist firebrand but another prominent U.S. firm - Arthur D. Little, the management experts from Cambridge, Mass.

The divergence of economics and politics is a familiar fact of current international life, but rarely is the contradiction as spectacular as this one. U.S. Ambassador to the United Nations Andrew Young, who has cited the Angolan and Cuban role in protecting Gulf in arguing against a Cold War perspective on Africa, was careful to say that the Angolan regime was "not doing us any favor" but taking the action because it needs the money.

Young in a recent interview with U.S. News & World Report, estimated the Gulf operations in Angola at "almost $1 billion worth of oil a year." A U.S. intelligence agency official told congressional sources that Gulf's payments to Angola are $600 million to $800 million yearly. Oil industry sources put the figure closer to $600 million. Gulf will give no current figure, but said Angola received tax and royalty payments from Gulf last year of $460 million.

In a statement furnished last week to the Africa subcommitte of the House International Relations Committee, Gulf said that "the cooperation of the government of Angola with Gulf in maintaining its production operation and in providing security for its employes and installation has been excellent." A Gulf spokesman in Pittsburgh said "we've had good relationships" in Angola and that employes have experienced "no trouble that is known" in pursing their jobs. According to the statement furnished to Congress, Gulf had 248 Angolan and 35 foreign employes in Angola as of April, including 23 Americans.

Indicating its optimism, Gulf reported to the House subcommittee that it plans to initiate new projects costing $83 million in its Angolan operations this year, with about half of the sum to be furnished by Angola under new contractual arrangements. The investments will include a "gas injection" system for existing wells and drilling for new offshore wells in the Atlantic. Such projects are usually undertaken only in situations where operations and return of capital over a long period of time are expected.

A senior State Department official dealing U.S. Policy in Africa said of Gulf's Angola operation, "Everybody knows it's there but it doesn't come up very much . It's taken for granted that this is going on . . . I guess it just shows that people can be pragmatic."

Despite the harsh comments of President Carter and other high officials about Angolan and Cuban responsibility for last month's cross-border attack on Zaire's Shaba Province, the State Department continues to advise U.S. businessmen, on a pragmatic level, that "we have no objection" to business deals and investments in Angola.

The Boeing Co., which sold several commerical jets to Angola and is installing air traffic control systems in Angola's network of commercial air-reports, is second to Gulf in U.S. business operations in the African country. Mobil Oil, Texaco, Cities Service and National Cash Register are also reported to do business there. And business sources said New York's Morgan Guaranty Bank recently held amicable discussions with Angola's ministry of finance about possible financial deals.

According to State Department officials, most of the companies operating in Angola would like to see the establishment of U.S. diplomatic relations in order to provide diplomatic services and protection there and to improve the climate for American business. Gulf, in its statement last week to the House subcommittee, also argued that U.S. diplomatic ties, by facilitating Angola's petroleum development, would "help to free it from economic and military dependence on non-African powers."

The nonrecognition of Angola is a notable exception to President Carter's general policy of seeking to have relationships and communications with friend and foe alike. Carter is reported to have told a prominent senator last year that the presence of the Cuban troops in large numbers was the only "hangup" in the way of diplomatic ties with Angola.

Carter said at a news conference Wednesday that the United States would "relish" the departure of the 20,000 Cuban troops estimated to be in Angola. But in the topsy-turvy world of Africa, a complete withdrawal of the Cubans might menace the interests of a U.S. corporation - Gulf.

The 2,000 or so Cuban troops in Cabinda, where Gulf is located, are on guard against the secessionist Front for the Liberation of the Enclave of Cabinda (FLEC), which is backed by Zaire, the major U.S. ally in the region. FLEC is reported to receive some support from French interests.

The forces backed by "ally" Zaire consider Gulf "enemy No. 1" after the Marxist Angolan regime itself, and would probably outst the company and replace it with a European firm if they ever have the chance.

In the meantime, "hostile" Angola with its Cuban troops makes certain Cabinda, oil-rich enclave of Angola where Gulf Oil has 125 offshore rigs that Gulf continues to pump oil, and that no harm comes to the American company or its employes.