To win computer business with the South Korean government, IBM allegedly delivered cash bribes in shopping bags.

In pursuit of Ni­ger­ian construction contracts, ­­Halliburton and its international business partners allegedly routed illicit payments through bank accounts in Switzerland and Monaco.

And a middleman for a middleman of the Italian energy company ENI allegedly made repeated trips to a Ni­ger­ian hotel room and handed over briefcases containing millions of dollars in U.S. currency to a government official. But paying the balance of the alleged $5 million bribe in the local currency was more problematic — the local bills were so bulky that the bagman allegedly had to deliver them by the carload.

These alleged schemes have come to light as part of an escalating effort by U.S. law enforcement officials against companies that engage in bribery abroad. Just last week, federal authorities announced they had charged IBM with corruptly pursuing contracts in Asia.

In recent years, the Justice Department and Securities and Exchange Commission have filed an increasing number of foreign corruption cases, charging companies such as Tyson Foods, General Electric, Alcatel-Lucent and Daimler, the maker of Mercedes-Benz cars and the former parent of Chrysler.

The cases reach from Latin America to Africa, Asia and the Middle East, involving contracts worth billions of dollars. Together, they suggest that illicit payments often tip the scales of global business — sometimes with the blessing of top corporate executives.

Corruption imposes “an enormous tax” on international business, said Lanny A. Breuer, head of the Justice Department’s criminal division, referring to the added costs companies must bear. “And because of that tax, jobs are lost” and “honest businesses lose business opportunities,” Breuer said.

Some U.S. companies have said that the Foreign Corrupt Practices Act (FCPA) of 1977 holds them to a higher standard than their overseas competitors — and that it can carry a price.

“[W]e operate in many parts of the world that have experienced governmental and commercial corruption to some degree and, in certain circumstances, strict compliance with anti-bribery laws may conflict with local customs and practices,” Diebold, an Ohio-based company whose products include automated teller machines, said in a recent regulatory filing.

Foreign companies that are not subject to the U.S. law “may be more likely to engage in activities prohibited by the FCPA, which could have a significant adverse impact on our ability to compete for business in such countries,” Diebold said.

The law also applies to foreign companies whose securities are traded in the United States.

Congress prohibited overseas bribery in the post-Watergate era. As a result of SEC investigations, hundreds of U.S. companies had admitted distributing money to foreign politicians, government employees and political parties, according to the Justice Department. The practice had been so accepted in the global marketplace that nations such as Germany, one of the world’s most developed countries, had allowed their companies to count foreign bribes as tax deductible.

The Justice Department took 48 enforcement actions under the FCPA in 2010, up from two in 2004, and the SEC took 26, up from three in 2004, according to a study by the law firm Gibson, Dunn & Crutcher.

The Justice Department ratcheted up its offensive with an FBI sting that led to 22 arrests early last year. The defendants, executives and employees of companies that sell military and law enforcement equipment, were led to think they were bribing the minister of defense of an African nation for a deal to equip the presidential guard, the Justice Department said.

As of last year, the Justice Department was conducting more than 150 criminal investigations under the FCPA, according to an international law enforcement report.

Multinational companies have reason to worry that employees in faraway offices will entangle them in trouble, but federal cases are alleging that the corruption sometimes reaches high into the executive ranks.

According to an enforcement action announced last month, executives at Tyson Foods realized in 2004 that they had a problem. A subsidiary in Mexico was paying the wives of Mexican inspectors for no-show jobs. The payments were meant to keep the inspectors from causing problems at meat processing factories, where they were responsible for making sure the meat was safe for export, according to court filings.

Tyson executives agreed that the payments had to stop. But one of the executives approved replacing them with payments to one of the inspectors, the SEC alleged.

Payments to an inspector continued for more than two more years, the SEC said.

Tyson settled with the Justice Department and the SEC last month, agreeing to pay $5.2 million. One of the executives involved was an “officer and senior executive” at Tyson, according to a court filing. But no Tyson personnel were charged or named in the enforcement actions. A company spokesman, Worth Sparkman, said in an e-mail that the employees involved were disciplined or have left the firm.

According to an SEC complaint in November, senior executives at Transocean, the oil services company, faced a predicament of their own in 2002. Faced with a local restriction on the amount of time the rigs could spend in Nigeria, the executives would have to suspend profitable drilling and move Transocean rigs out of the country or risk severe penalties.

Transocean allegedly chose a third option: It pretended to remove the rigs, and it paid foreign customs officials to fabricate documents showing that the equipment was gone.

The SEC said an executive vice president at Transocean justified the “paper moves” as necessary to avoid an interruption in drilling.

Transocean, owner of the Deepwater Horizon rig that exploded in the Gulf of Mexico, agreed to pay $20.7 million to settle allegations that it made illicit payments from 2002 to 2007, according to the SEC. A company spokesman declined to comment for this article.

In January, the SEC alleged that a former chief executive of Innospec, a manufacturer of fuel additives, personally approved the bribing of officials in Iraq.

A go-between in the alleged bribery copied then-chief executive Paul W. Jennings on a 2005 e-mail reporting that Iraqi officials were demanding a 2 percent kickback, the SEC said in a lawsuit.

“We are sharing most of our profits with Iraqi officials. Otherwise, our business will stop and we will lose the market,” the middleman wrote, according to the lawsuit.

Some of the alleged bribes were used to ensure that a competitor’s product failed a field test, the SEC said.

The Innospec case also shed light on the economics of bribery. Altogether, from 2000 through 2008, Innospec made or promised illicit payments of $9.2 million in Iraq and Indonesia in return for contracts worth $60.1 million in profit, the SEC alleged. For Jennings, bonuses of $116,092 were tied to sales procured through bribery.

The middleman pleaded guilty to bribery last year, and Jennings settled the SEC case without admitting or denying wrongdoing. Jennings agreed to pay $229,037 in penalties, interest and the forfeiture of ill-gotten gains.

Innospec’s general counsel, David Williams, said the company has a new management team “and enhanced compliance programs.”

By one measure, the alleged crime paid off. In a settlement last year with authorities in the United States and Britain, Innospec agreed to pay $40.2 million, less than it is said to have profited from the bribes.

Innospec argued and authorities agreed that the total was the most it could afford.