Before getting down to work Tuesday, Soviet arms inspectors enjoyed a Fourth of July parade but were puzzled by the fezzes worn by Shriners.

The Soviet technicians are in Salt Lake City to begin inspections under terms of the Intermediate Nuclear Forces Treaty that bans medium-range nuclear missiles.They will inspect vehicles leaving Hercules' plant southwest of Salt Lake City to make sure no more Pershing 2 missile motors are being produced.

Their work started Tuesday, but on Monday American escorts took 10 of the 23 Soviet team members to the suburb of Murray to see the parade.

A pink-haired lady clown who threw kisses to the Soviets drew the most return waves, and the Soviets also enjoyed watching gymnasts working out on portable bars on a flatbed truck. Children, any age, were their favorites.

But there was the trouble with the fezzes.

"Uh, they're Shriners," a State Department interpreter offered. "It's like a fraternity."

"Yes, but why the Turkish hats? Are they Moslems?"

A reporter said the dress goes back to the Middle Ages, and "actually we're not supposed to tell. It's a state secret."