Members of the Soviet arms inspection team in Utah say establishing trust and laying groundwork for future nuclear weapons treaties within "the spirit of glasnost" is the most vital aspect of their United States assignment.

Members of the 30-member Soviet delegation based at Hercules Inc.'s plant here say working closely with the United States to verify the treaty is like "tending to our common baby."Their American counterparts with the On-site Inspection Agency agree that crucial precedents are being set. "We may be writing the first page in the book of peace," said Cmdr. Kendall Pease, agency spokesman.

"Our presence here is important not only to the INF treaty. The way our cooperation in this sphere works is also important for the future of Soviet-American agreements on disarmament. The INF treaty is the first step on a long road to disarmament, and thus it is very important for us to take every possible step to ensure the implementation of the treaty," said Vladimir Zhukov, spokesman and interpreter for the team.

Zhukov 41, an 18-year veteran of the Soviet Foreign Ministry, came to Utah on July 2 as the public affairs officer. The team now operates the only permanent monitoring facility in the United States allowing the Soviets to make sure no Pershing 2 rocket motors are produced at the Bacchus East Plant of defense contractor Hercules.

Hercules formerly produced the rocket motors at its Bacchus East Plant in West Valley City southwest of Salt Lake City.

Under the INF treaty, while the Soviets monitor Hercules, a U.S. inspection team is performing the same tasks in Votkinsk near the Russian Ural mountains, assuring America that SS-20 missiles are not being produced there.

The treaty, signed by President Reagan and Soviet leader Mikhail S. Gorbachev on Dec. treaty specifies that all nuclear missiles in the two superpower arsenals with a range of roughly 300 miles to 3,500 miles be destroyed within three years.

Lt. Cmdr. Jim Szatkowski, 35, site commander for the OSIA's Magna Portal Detachment, said "there's a strong feeling that one of the most important thing's going on here is that we are establishing a precedent.

"We're very sensitive to that issue," he said. "What we're doing does tend to establish the groundwork for future activities for arms control, and as such we are being careful in what we do and how we do it as well as how it is interpreted later on."

Szatkowski, a naval engineer, was assigned to the OSIA in February and said his primary goal is making the treaty work by ensuring that the Soviets are able to perform their tasks of verification.

Szatkowski meets several times each week with Soviet team leader Anatoli Samarin. He characterizes the meeting as formal, adding that each side is watching itself to guarantee its own strict compliance with the treaty.

"Between the two chiefs it's quite a formal discussion. We sit across a table and take turns at addressing our concerns and establishing resolution of those concerns," Szatkowski said.

On other levels, the two groups work under a professional but less formal atmosphere without what Szatkowski calls "undue closeness."

"I have people on my staff that discuss technical matters with his (Samarin's) staff," Szatkowski said. "He has a technical manager who works with my technical manager. He has a logistics type who works with my logistics guy. He has a public affairs guy who meets with my public affairs guy. Those relations are much less formal."

Szatkowski refused to speculate on whether the Soviets might seek to gain data not specifically outlined in the treaty. "Any comment about that would be inappropriate. To say that they wouldn't be observant would be naive. But on the other hand, it does appear that the ones who are here are here to do their job, which is to monitor the portal and to report back what they see."

Zhukov said that he doesn't expect either side to violate the treaty. Both sides are working in good faith, he said.

"This first experience might be used to a great extent as a framework for a working document for both sides while working on the verification procedures for other disarmament treaties," he said.

Asked if the kinds of protocols that are developed could be applied to treaties as diverse as those concerning chemical weapons, Zhukov replied, "Naturally, that might be a little different for chemical weapons. There might be on-site inspections; there might not. It depends on the kind of treaty we might achieve. There are some provisions that can't be accepted on the basis of trust.

While they have been in Utah, the Soviet team has been besieged with requests for speaking engagements and press interviews. Szatkowski says he is getting two or three requests a day from people seeking access to the Soviets.

"There's little interest in the Soviet press in our inspectors (in Votkinsk), but that may increase," he said. "People aren't scrambling like they are here. But that might change. "There's a lot of timidity, if you will, toward a new situation."