A bitter, century-old dispute between the Navajo and Hopi over thousands of acres of Arizona desert, where each tribe wants to live, worship, and graze its herds, has surfaced in Congress again, this time over a desolate range of sandstone plateaus known as Big Mountain.

A 1974 law split 1.8 million acres between the tribes, who have been feuding over scarce grazing land and water. Under the law, about 8,000 Navajo and 100 Hopi living on the wrong side of the dividing line were ordered to move to the other side or to one of the nearby towns.

The Navajo have been desperately battling relocation ever since, despite federal benefits to those affected, including three-bedroom houses worth $66,000 and $5,000 "incentive bonuses."

So far, 400 Navajo families and 11 Hopi families have moved, at a cost to the government of $35 million. Costs are expected to reach $180 million by the time the program ends in 1986.

Among the areas the law placed under Hopi control was Big Mountain. Sen. Barry Goldwater (R-Ariz.), caught for years in the cross fire between the tribes, promised to try to help the 100 Navajo families who would be forced to leave the spot, which Navajo tradition holds sacred.

Goldwater introduced legislation last year to swap that land with the Hopi in exchange for 16 Navajo parcels.

But both tribes opposed the bill at hearings two weeks ago, and the hostility between the two appeared as intense as ever.

The Hopi accuse the Navajo, a nomadic tribe of sheepherders who moved into the area in the 15th century, of preventing the Hopi from using their half of the territory, of shooting at Hopi crews building boundary fences and of marauding their land and stealing sheep and cattle. Navajo leaders, they charge, have misled their people about the resettlement program in order to frustrate relocation.

The Navajo, who outnumber the Hopi by about 150,000 to 8,000, believe that the divided land belongs to them. They decry the relocation program for cruelly uprooting from their ancestral homes elderly and traditional Indians who are unable to adjust to life elsewhere.

"I wish that the Hopi officials would begin to realize that these people who are subject to relocation are human beings," said Percy Deal, director of the Navajo's land dispute office.

"They are not mechanically controlled where you throw one switch and they begin to relocate and you throw another switch and they stop complaining," he said. "There's so much pressure and agony that they have to go through."

The battle between the two tribes started in 1882 when President Chester A. Arthur established a 2.5 million-acre reservation for the use of the Hopi "and such other Indians as the Secretary of the Interior may see fit to settle thereon." The Navajo population then skyrocketed, crowding out the Hopi and leaving them little land beyond the pueblo cities they had built on desert mesas.

Later court battles--which reached the Supreme Court--held that the Hopi had exclusive right to an area of 600,000 acres in the middle of the reservation, but that the tribes had to share the 1.8 million acres eventually divided by the 1974 law.

The tribes are fighting their old war with modern weapons. The Hopi have retained a public relations firm in addition to a battery of lawyers. And the wealthy Navajo have launched a $2 million lobbying, media and legal campaign "to ask the American taxpayers whether they want to see their tax dollars spent to make a group of people worse off than they are now," Deal said.

The skirmish over Goldwater's bill typified the slippery nature of the struggle. The bill defines Big Mountain as an area of 20,480 acres, inhabited by about 450 Navajo.

But the Navajo argue that the actual size of what they consider Big Mountain totals 192,000 acres and 361 families, and that the lands Goldwater proposes to trade are also inhabited by Navajo, some of whom would be forced to relocate for a second or even third time.

The bill, Navajo tribal chairman Peter MacDonald told the July 13 hearing, would simply be "exchanging miseries at an increased cost to the federal government."

The Hopi, meanwhile, contend that there are only about 27 Navajo families on Big Mountain. They also object to the bill, not so much for the substance of the trade as for the idea that the federal government could impose the deal on them.

The Hopi don't want to settle for cash. They have rebuffed a $117 million offer from the Navajo, who earn more than $40 million a year from oil, coal and natural gas leases, to buy their share of the reservation.

"Hopi land is sacred to the Hopi people," Hopi lawyer John Kennedy told the hearing. "The Hopis would no more trade their reservation for money than would the Israelis sell Jerusalem."

MacDonald, who once vowed that the Navajo "will resist their eviction to the point of violence, in effect causing another civil war," promised Goldwater to try to reach an agreement with the Hopi within the next 45 days to resolve the Big Mountain problem and minimize the number of other moves required.

Goldwater and fellow Arizona Sen. Dennis DeConcini (D) sent a letter to the chairman of both tribes after the hearing, threatening "to pursue legislation should the two tribes not be able to reach a land exchange agreement in a reasonable amount of time," and saying that representives from their offices would attend the next negotiation session.

One unsettled question is exactly what the government will do about any Navajo remaining on Hopi land after the voluntary resettlement ends in 1986.

Steve Goodrich, executive director of the government's Navajo & Hopi Indian Relocation Commission, said, "After that date I don't think anyone really knows what will happen."