Nestled in a valley surrounded by rocky ridges right in the middle of the vast Australian outback lie six silvery-white spheres that look like huge golf balls.

They are the main features of a top-secret U.S.-Australian intelligence operation officially named the Joint Defense Space Research Facility. Unofficially, residents of nearby Alice Springs call it "the space base." Some worry that it makes their out-of-the-way but fun-loving little town -- scene of what is probably the world's only dry-riverbed boat race -- a nuclear target.

That thought is a bit unsettling to some Australians since their remote "down under" continent otherwise must be one of the world's safest places in the event of a U.S.-Soviet nuclear conflict.

The facility's six "radomes" house sophisticated antennas that receive a variety of signals, intelligence and communications from U.S. spy satellites, mainly on Soviet missile tests.

Positioned to intercept the telemetry from Soviet rocket launches and pick up Soviet and Chinese military communications, the satellites cannot transmit effectively to the United States because of the earth's curvature, according to Australian experts. This is the best place to receive the signals.

Accordingly, security is tight. Although the radomes are visible from the air, planes are not allowed to fly directly over Pine Gap. Two security fences bound the facility, and Australian police politely but firmly refuse entry to visitors at a checkpoint well out of sight of the installations.

The Pine Gap station and a complementary one at Nurrungar, South Australia, that is linked to the main U.S. early warning satellite system, represent America's biggest and most vital such installations outside the United States. They also symbolize the traditionally close U.S.-Australian defense relationship.

Despite periodic outbursts of criticism, that relationship appears to be growing closer. This month elements of all four U.S. service branches joined Australian and New Zealand forces in the most sophisticated and one of the biggest joint military exercises ever staged here.

Among the 100 aircraft participating in the three-week Kangaroo 81 exercises now under way, along with 20,000 servicemen and 25 ships, will be American B52 bombers based on Guam. Earlier this year the Australian and U.S. governments concluded an agreement allowing unarmed B52s to land at Darwin in Northern Australia in connection with sea surveillance over the Indian Ocean and navigational training.

Last week the Australian government decided to buy 75 U.S.-built McDonnell Douglas F18 jet fighters in a $2.5 billion deal to replace the country's aging French-supplied Mirage 30s.

Although Australia's military relationship with the United States, particularly regarding the U.S. installations and B52 activities, has been denounced by the left wing of the opposition Labor Party and other radical government critics, recent opinion polls show that a large majority of Australians approve of these operations. According to a survey published in June, 60 percent of voters favored the presence of the U.S. installations in Australia, 22 percent were opposed and 18 percent either had no opinion or did not care.

The same survey showed 58 percent of voters agreeing with the government's decision to allow U.S. B52s to use Darwin as a staging point for reconnaissance flights.

Besides the Pine Gap facility, the others are the North West Cape Naval Communications Station in the state of West Australia, the Tranet Station at Smithfield in South Australia and the Joint Defense Space Communications Station at Nurrungar.

The Australian Defense Department strongly defends the stations, arguing that all now have Australian participation and share their information with the Canberra government.

"We derive quite a lot of benefit ourselves," said Ross Thomas, an assistant defense secretary for strategic and international policy, in an interview in the Australian capital. "They're not just facilities that exist to support U.S. interests."

More sensitive is the question of whether the presence of the stations makes Australia a Soviet nuclear target. The government's position is that it does not consider any of the facilities nuclear targets except possibly in the event of a general nuclear war.

The Soviet ambassador to Canberrra contributed to the debate in March, when he told reporters Australia "could become a nuclear target" because of the B52 agreement and reported proposals to base U.S. warships near Perth and expand the Pine Gap facility.

However, in Alice Springs (population 17,000), 12 miles northeast of Pine Gap, Roger Vale has "never detected any apprehension by the community" at the presence of the space base, which has been operational since 1970. A conservative member of the Northern Territory legislature, Vale said he thought the nuclear target claim was "all guesswork" put forward by leftist groups.

Vale added that demonstrations against the station -- the most recent drew about 100 persons -- "represent a very, very minute section of the population overreacting to it."

Ian Yule, an administrator of an aboriginal school and a member of a local left-leaning outfit known as the Peace Group, takes a different view.

"People here are not too keen on Alice Springs being a nuclear target," he said. He also condemned the secrecy surrounding the base, saying that "in a democracy we have a right to know what its functions are."

Even critics like Yule agree, however, that the approximately 240 Americans employed at Pine Gap -- mostly by the Central Intelligence Agency, the National Security Agency and their contractors -- have been "model citizens."

Said Vale of the Americans, "I can't think of any other group more amenable to mixing with the community." Pine Gap even enters the annual Todd River "regatta," called Henley-on-Todd, in which participants in bottomless boats run along the dry river bed cheered on by spectators amid great consumption of alcohol.

A leading Australian expert on the U.S. installations, Desmond Ball, said he thought there was no doubt that the Pine Gap facility makes Australia a target for Soviet nuclear attack.

"Soviet doctrine," he said, "is to hit critical intelligence capabilities."

A senior research fellow at the Strategic and Defense Studies Center of Canberra's Australian National University, Ball argues in a book published late last year that the United States has taken Australia for granted and treated its people and interests with "disdain" in establishing and running the U.S. stations here.

Ball calls for an "informed public debate" on the bases, but he stops short of demanding the bases' removal.

Ball sees reaction against the U.S. installations ebbing and flowing with other factors.

"At the moment it's at one of its peaks again," he said. He cited fears of being tied up in "growing cold-war tension" between the Reagan administration and the Soviet Union.

For the opposition's part, the leader of the Labor Party earlier this year toured the main installations and gave all but one a clean bill of health. The only one he complained about -- oddly, in the view of government officials -- was the naval communications station at North West Cape.

The opposition leader, Bill Hayden, said he wanted the United States to secure Australian consent "for all orders to initiate military action which flow from the station" and to guarantee "that the station will not be used to send orders for a first-strike nuclear attack nor to initiate a limited strike."

The Australian defense minister, Jim Killen, rejected the demands as "ill-founded and unsound" and said that because of multiple channels and automatic switching equipment in the complex U.S. defense communications system there was no way to stop such messages without shutting the North West Cape station down entirely.

Hayden did not mention allegations by some Labor Party members and leftist groups that the sophisticated electronic equipment at Pine Gap has been used in the past to monitor domestic communications in Australia.

"Some people feel the Pine Gap installation represents an ability to carry out intelligence activities inside Australia," said Robert O'Neill, the head of the Strategic and Defense Studies Center in Canberra. "I can't see why they the Pine Gap operators would want to do it, but it does make some people in Australia paranoid because they have to take it on trust. And there are people who don't trust the U.S."