When Australian Prime Minister Robert Hawke meets with New Zealand Prime Minister David Lange next month, it will be the first time the two nations have ever found it necessary to define the relationships between the only two western nations in the area.

The meeting, political analysts say, reflects a chasm that has opened between the two countries since New Zealand triggered the crisis in the mutual defense alliance linking Australia, New Zealand and the United States by banning U.S. nuclear-powered or nuclear-armed warships.

Both Australia and New Zealand, junior partners in the 34-year-old ANZUS treaty, insist that it still exists. But that is where agreement ends. Lange recently said in Geneva that ANZUS would be "alive and kicking" if one partner was attacked.

But, while Hawke agrees with the official U.S. view that the treaty still exists formally, for all practical purposes, he says, it is now ineffective and will remain so while New Zealand maintains its ban on U.S. warships.

Hawke has announced the indefinite postponement of this year's ANZUS council meeting. He has described the treaty as "inoperative" and said that until "normal operations" can be resumed under the treaty, Australia will rely on "appropriate bilateral arrangements" to protect its interests.

With the drastic curtailment in military cooperation and intelligence sharing between the United States and New Zealand, Hawke has pledged that Australia will pass on to New Zealand none of the information it gets from Australia's continuing intelligence links with the United States, but will otherwise continue its links on that level with its friend across the Tasman Sea.

Australia is expected to take over New Zealand's main contribution to the alliance's intelligence pool -- monitoring Soviet warships in the Pacific and Indian oceans -- from a base in Singapore.

The ANZUS storm has created the biggest foreign affairs row in Australia and New Zealand since their involvement in the Vietnam War in the late 1960s.

Opposition leader Andrew Peacock, who was foreign minister for five years during the previous conservative government of Malcolm Fraser, has accused Hawke of being unable to keep the alliance afloat because of pressure from the left wing of Hawke's ruling Labor Party.

Nobody in Hawke's party doubts his personal commitment to maintaining a defense alliance with the United States or his total opposition to having Australia follow New Zealand's lead and banning nuclear warships from Australian ports.

American nuclear-powered warships and naval units capable of carrying nuclear weapons are frequent visitors to Australian ports.

The U.S. ship which triggered the New Zealand ban, the USS Buchanan, has spent most of last week moored in Sydney harbor.

Australia also permits American B52 bombers on training and navigation exercises to fly over Australia and land here. Three important American bases that receive military and intelligence information from U.S. defense satellites and transmit orders to American nuclear submarines are located in Australia. Hawke emphasized several times last week that all these arrangements would remain.

Indeed, he said they were so important that staving off any threat to their continuance was the reason he changed his mind during talks in Washington last month and withdrew from an Australian commitment by the previous government to provide logistical assistance to the United States when and if it tests the new MX missile in South Pacific waters later this year.

A decision to provide the assistance in the MX tests would have provoked a fight that would have strengthened the antinuclear forces within Hawke's ruling Labor Party, political analysts said.

His determination to forestall the left-wing pressures that have shaped New Zealand's antinuclear policy was emphasized in a recent television interview marking the second anniversary of being sworn in as Australia's prime minister.

He said he would refuse to lead an Australian government that withdrew support for the country's alliance with the United States.

It was a significant threat, because it is Hawke's personal popularity that led Labor into power in 1983 and saw it reelected last Dec. 1 with a reduced but still substantial majority.

"The MX assistance was a minor, passing thing," Hawke said. "But what was put potentially at risk was first of all the support that I and my government have not only within the party, but more broadly, for the centrality of the U.S-Australia alliance and what goes with it -- the hosting of the joint facilities in Australia and the visits of American ships to our ports."

Hawke said Australia would take bilateral steps to maintain the country's defense links with the United States while taking separate, bilateral links to maintain defense cooperation with New Zealand. Details of how to conduct that delicate diplomacy are to be announced shortly.

For the American links, Australian government sources said they believe U.S. Secretary of State George P. Shultz will visit here in midyear to emphasize the continuing U.S.-Australian cooperation and that there will be an escalation in the regular contact between defense officials of both countries.

It will be more difficult for Australia to prove that it is not abandoning New Zealand and at the same time support the U.S. displeasure with New Zealand's antinuclear policy without appearing to bully or influence the New Zealanders.

The Hawke talks with Lange will go to that central point. The problem is likely to be compounded by a marked difference in each country's perception of external threat.

Australia, with Indonesia, China and Japan as its neighbors to the north, is much more conscious of a security threat. But New Zealand's isolation makes it feel less threatened.

The only two past meetings between Hawke and Lange -- in Papua New Guinea and Kiribati last year -- were brief and, according to insiders, stiff. Their lack of personal rapport will add to the complicated task they already have of seeking a formula to persuade both Australians and New Zealanders that the ANZUS treaty is worth more than the paper it is written on.