Just picture it: a band of armed rangers, floating down the Colorado River. On the rocky bank, the spot several long-eared burros. they scramble ashore, and shoot the animals with tranquilizer darts. The burros stagger and fall. One dies, although a ranger tries mouth-to-mouth resuscitation.Another burro is flown out of the canyon wrapped in a cargo net dangling from a helicopter.

It really happened.

For the past three years, National Park Service officials have searched for a way to rid the Grand Canyon of some 300 wild African burros, descendents of pack animals turned loose by propsectors after the Gold Rush a century and a quarter ago.

The tale of how they've tried, and have become entangled in an emotional battle with animal lovers has unfolded like a comedy of the absurd, poignant at times, and slapstick too. Only the players take it seriously.

The focus of the controversy is the Park Service's voluminous "Federal Burro Management and Ecosystem Restoration Plan and Environmental Statement," in which the preferred option is "direct reduction."

"Shooting," explained park official James E. Walters, "is an inflammatory word."

Euphemisms aside, shooting is exactly what the government wants to do to these feisty little animals who are chomping their way through the canyon's sparse vegetation, trampling archeological sites, eroding steep slopes with their crisscrossing trails and competing for food with the majestic bighorn sheep.

"How can we let the Grand Canyon, one of the seven natural wonders of the world, be ruined by a few jackasses?" demands one Park Service man.

The only problem is those 12,000 letters from plaintive schoolchildren that Interior Secretary Cecil D. Andrus received when "direct reduction" was first proposed three years ago. Not to mention the lawsuit filed by animal protection groups, forcing him to write a detailed environmental impact statement, do scientific studies and hold public hearings.

All the paperwork, hearings and studies, including the one examining the feasibility of helicopter removal, only bolstered the Park Service's determination to shoot the burros. It had just about been decided again this year.

Then, enter Cleveland Amory, author and head of the New York-based fund for Animals, backed by a board of directors with the likes of Katharine Hepburn, the princess of Monaco, Mary Tyler Moore and Andrew Wyeth.

"Burros ar very, very nice animals," Amory says. "Any donkey is interesting. We shouldn't suddenly decide, 80 years after the Gold Rush, to slaughter them."

The fund has wangled Park Service permission, provided Andrus agrees, to hire five cowboys, 20 horses and five mules and build corrals to herd the burros and drive them up and over the steep slopes of the canyon. The Park Service had dismissed this alternative as too expensive and laborious. But the fund says it will spend $120,000 of its own money, a third of what the government thinks it will cost.

"The fund will undertake a national campaign asking the children of America to help Uncle Sam and the fund for animals to save the Grand Canyon burros," the fund wrote Walters. "This is appropriate in the Year of the Child, and will reflect favorably on the National Park Service and the Fund for Animals."

The 300 burros would be adopted. "We get a call a day from people wanting a burro," Amory said. "Even people in Brooklyn . . . You'd love a burro. It's better than a husband.

Grand Canyon Superintendent Merle Stitt has a skeptical twinkle in his eye. "If they can get those burros out live, horray!" Stitt would give the fund 60 days to do it, and, if it doesn't work, sharpshooters would take over.

The burro battle has split the environmental movement. The Sierra Club, the National Wildlife Federation, the National Audubon Society all support the shooting of the burros. But groups such as the Humane Society of the United States, the American Horse Protection Association and the Committee to Save the Grand Canyon Burros are likely to file suit against the Park Service's new proposal, perhaps even opposing Amory's scheme on ground that burros should remain part of the scenic and historic environment of the canyon.

Although mules are now the tourists' pack animal, burros should be preserved as part of the romance of the West for their roles in developing mines, building railroads, settling towns and serving poineers, humane groups contend.

The issue has also divided scientists. Park Service experts claim that the burro, imported by the Spandiards in the 16th century, is an exoitic animal, not native to the area. Like wild goats on San Clemente Island and wild boars in the Great Smokies, they say, burros should be eradicated for wreaking havoc on an alien ecosystem.

However, Paul S. Martin of the 1niversity of Arizona sees burros as the restoration of a species hunted to extinction by aboriginal man in the Plenistocene era. "Burro-sized equids were definitely native to the Grand Canyon," contends Martin, who found a 26,000-year-old burro-type hoof in a pile of ancient sloth dung in a Grand Canyon cave.

The park Service counters by saying the park should "maintain a vignette of primitive America found at the coming of European man."

The issue could be crucial in the coming legal battle. The Washington law firm of McCandless and Barrett, representing the American Horse Protection Association wrote the Park service the "This culturally egocentric view is an outrage . . . The policy is not to restore the park to its state before man as a species inhabited North America; only western man counts."

The burros' effect on the park's ecology is "infinitesimal," McCandless and Barrett contended. "The burros . . . are merely reoccupying a biological-ecological niche vacated by identical ancestors approximately 10,000 years ago."

Meanwhile, hundreds of citizens have volunteered their own solutions in recent months. One man said the burros should be sent back to Africa. Other suggestions include importing mountain lions to eat them, growing grass in the canyon to feed them, giving them to prisoners to help rehabilitation, giving them to old folks for pets, giving them to American Indians to eat, giving them to Mexico.

The Park Service has earnestly investigated at least some of these possibilities. Dr. Antonio Landazuri Ortiz, in a letter reproduced in the draft environmental statement, politely declined on behalf of the Mexican government, adding, "but we appreciate your offer."

The Park Service also gave due consideration to the suggestion by Washington's Christine G. Stevens and other animal lobbyists that the burros, known for their active sex life, be sterilized so they can die out naturally.

"Possible sterilization techniques include the use of chemosterilants administered orally or by injection, mechanical castration, irradiation and ultrasonics," the statement said. "Each of these techniques had advantages and disadvantages.""

Other ideas are more general. Diane S. Loughlin of Stamford, Conn., writes, "Perhaps Mobil Oil, some rock star or a rich Arab can be called upon to help with Project Air Burro lift. Can't the United Nations or the Peace Corps come up with some solution?"

Native southwesterners, who've lived with burros all their lives, are less sentimental. "The burro tramples, urinates and defecates in and around water," an Arizona Republic colunmist wrote. "Wild Jacks have been known to attack humans, particularly women."