The latest trophy in the U.S. Fish and Wildlife Service's hunt for corporations willing to help it protect the nation's wildlife is E.I. du Pont de Nemours & Co., which yesterday announced it would donate $50,000 to federal efforts to breed bald eagles in captivity.

The contribution by Du Pont, one of the nation's largest chemical and petroleum conglomerates, is believed to be the first direct contribution by a major U.S. corporation to a fish and wildlife program. But officials at the Interior Department agency hope that where Du Pont leads, other corporations will follow soon.

"It is unusual for the Fish and Wildlife Service to receive this type of support from a private company for a project that has no direct relationship or benefit to the company's business activities," said agency Director Robert A. Jantzen, who, with Du Pont Executive Vice President Robert J. Richardson, announced the grant at Patuxent Wildlife Research Center near Laurel.

Richardson said that Du Pont, whose subsidiaries include Consolidation Coal and Remington Arms, selected the bald eagle program because "it is an effort to which our employes and the public can relate." But he deflected a suggestion that the company was attempting to atone for damage done by a former Du Pont product--DDT.

The pesticide, which was in wide use after World War II, causes birds to lay thin-shelled eggs that break before chicks can hatch. Until it was banned for general use in 1972 the pesticide was responsible for sharp declines in the numbers of several species of birds. Among them was the bald eagle, now listed as endangered in 43 states.

Du Pont got out of the DDT business in the mid-1950s for "commercial reasons," Richardson said yesterday. The bald eagle grant, he said, "has nothing to do with our production in ancient days of DDT."

Since 1976, the Patuxent center has placed 44 capitivity-bred eaglets in adoptive homes in the wild, with 95 percent being accepted into their nests. Demand far outstrips supply, however. Officials hope the Du Pont grant, which may be renewed, will enable them to increase the number of breeding birds.

For the Fish and Wildlife Service, the grant is the crowning jewel in a relatively new campaign to attract corporate interest and money in support of its activities. As recently as the mid-1970s, the agency turned down an offer from the late Jack Webb, who was so enthralled by the story of the snail darter that he wanted to produce a television series based on the agency.

But while officials acknowledge that their interest in private industry contributions "is compatible with the philosophy of President Reagan," the effort got its start in 1978, when an experimental agreement with Joseph E. Seagram & Sons Inc., the makers of Eagle Rare bourbon, far exceeded the agency's expectations.

The Eagle Rare brand prominently features the bald eagle in its ads, and the company has purchased and distributed thousands of brochures on the plight of the national bird.

Since then, the agency has entered into similar relationships with a wide variety of businesses, ranging from clothing manufacturers to the Indiana coffin maker that agreed to plant a tree in a national forest in memory of each person laid to rest in one of the firm's products.

"We need a lot of help from outside to support legitimate projects," said agency spokesman Alan Levitt. "There's a public misunderstanding of wildlife management. Seventy-five percent of the American people think coyotes are endangered. Some people think a manatee a seal-like animal is an insect. You know, a praying manatee?" He said he doesn't mind that the agency's corporate sponsors prefer to promote the more sympathetic fauna, such as the bald eagle. "All of these companies are taking the sexy species," he said. "But we can spend the agency's our funds on the creepy-crawlies."