In the summer of 1988, barely three months in office, Postmaster General Anthony M. Frank proposed "a bold stroke" to then-Treasury Secretary James A. Baker III.

Frank wanted to end one of the federal government's longest running unwritten interagency agreements, one that had given treasury's Bureau of Engraving and Printing a virtual monopoly over the nation's stamp production.

He suggested that stamp issues be divided among three or four private printers and a new "government-owned" plant that a private contractor would operate, using the bureau's presses, but under U.S. Postal Service supervision.

Frank's proposal arrived at the bureau's 14th Street plant in the midst of what the General Accounting Office has described as a sharp and bitter feud that already had threatened the bureau's future as a stamp producer. By law, the bureau is required to print the nation's paper money, but in practice it also has printed almost all the nation's stamps since 1894.

In recent years, however, relations between the Postal Service and the bureau deteriorated to the point that key officials would not talk to each other. Bureau officials say the postal officials treated them shabbily, as if they were a job printer, not an equal partner in what they regard as a highly skilled craft.

Citing that "tenuous" relationship, the GAO appealed last December to Frank and Treasury Secretary Nicholas F. Brady to resolve questions about the future of stamp production.

Yesterday officials of the Bureau of Engraving and Postal Service neared final agreement on their first formal contract, a pact that officials close to the negotiations say should assure the bureau a major role in producing the nation's stamps for the next five years.

The agreement will provide written guidelines for the production of stamps and will require that postal officials give the bureau advance notice of the stamps it wants.

But the contract also will force the Postal Service to rely increasingly on private printers to meet the soaring demand for stamps and some of those printers may be overseas, postal spokesmen have acknowledged.

The prospect of U.S. stamps being printed in foreign lands has infuriated some stamp collectors. "That's just lunacy. It's politically unrealistic and will never happen," said Michael Laurence, editor of Linn's Stamp News, the country's biggest philatelic newspaper.

Postal officials declined to discuss details of the new agreement, but Charles Yeager, Linn's Washington correspondent and a specialist on stamp production, said he doubts the service can find enough private printers capable of handling the added work the contract envisions.

Donald M. McDowell, the Postal Service's director of stamps, rejected Yeager's warning. "You can rest assured we will not commit to stamp production outside in the private sector without the assurance that the capacity is there," McDowell said.

"It's not hard to find someone who can print those stamps. There is an overcapacity in the printing industry," he said. What is difficult to find are printers who can print stamps and handle the processing "downstream"; that is, adding the perforations and forming the stamps into booklets and coils, McDowell said.

The Postal Service began to turn to private printers in 1979. McDowell said that one advantage of the new agreement is that it will offer private printers a certainty that they can win a percentage of the stamp business. Without that, many printers would be unlikely to invest in the machinery needed for stamp production, he said.

Earlier this spring, the Postal Service published a notice declaring it expects 50 percent of its stamp production will be in private hands by 1994 and appealed to foreign, as well as U.S. companies, to respond. McDowell said that under the "Buy America" Act, any foreign printer would be have to meet some difficult requirements, but that it is possible that a foreign company could meet the Postal Service's requirement for the "lowest responsive bid."

During the secret contract negotiations that began in late February, the Postal Service rejected bureau proposals to produce all U.S. stamps, according to an individual familiar with the talks. He said the negotiators envision that about 20 percent of stamp production will be handled by private firms, almost double the current level, but less than the 50 percent the Postal Service had suggested.

Ira Polikoff, a spokesman for the Bureau of Engraving, said officials there believe the contract will be good "for both sides." He said the agreement should end the bickering "forever" and should assure the nation of a continuing supply of high quality stamps at an economical price.

The 600 bureau workers who specialize in stamp production will be "fully employed . . . as busy as ever," he said.

McDowell said the Postal Service looks to the agreement "with great enthusiasm." It should be the foundation "upon which a mutually beneficial business relationship can rest," he said.