The fur flew and tempers flared at two inaugural balls early yesterday morning when throngs of Republican revelers got ready to go home and then couldn't find -- or couldn't get their hands on -- their minks and lesser wraps.

Accounts differ on just how the coat snafu and subsequent fracas developed, but on this much there is agreement: Some people, despite the frigid weather, left the balls coatless. And other people marched out onto the icy streets in coats, furs and stoles that didn't belong to them.

"A lot of mink stoles look the same," Max Krupo, D.C. deputy police chief, said, trying to explain the mix-up. "The normal person couldn't tell the difference."

Though police were giving coat snatchers the benefit of the doubt, one mink stole was reported stolen from a ballroom while its owner was dancing. And there were some callers yesterday, according to an attendant, who admitted "borrowing" the fur coats on purpose but quickly arranged their return.

Krupo said police got caught up in the great coat caper after inaugural ball crowds at the Washington Convention Center made a run on the coat rooms shortly after midnight. Many people waited an hour or more for attendants to retrieve their wraps. But a few got tired of waiting and turned so rowdy -- screaming in frustration and shoving coat check attendants aside to look for the coats themselves -- that police were called.

"It was awful, a little frightening, actually," said Rebekah Liller, an aerospace company employe and a guest at the ball. "You could really feel the tension."

Liller, who saw one man leap over the counter to get his own coat, finally gave up and went home, returning to the convention center yesterday afternoon to reclaim her leather coat.

She was lucky.

At the D.C. Armory, site of the Reagan Youth Ball, Randy Broberg and one of his coworkers in Rep. William Lowery's (R-Calif.) office said they couldn't even check their coats and had lost them by the end of the evening.

"The coat checks filled up by 8:30 p.m., and hundreds and hundreds of coats were strewn on the bleachers and benches," said Broberg, who stuffed his $270 coat and his companion's in a nook behind a bleacher.

When he got ready to go home, he said both garments were gone.

"Having drunk all night, people just walked off with the wrong coats. . . . It was chaos," said Broberg, who joined a long line yesterday at the Armory's lost-and-found office to fill out description forms.

Broberg estimated that 50 to 60 people, including five he met in the lost-and-found line, are still without their coats.

Armory board officials acknowledged that keys and wallets have been reported missing but said that only one coat was taken.

Officials at the convention center, which hosted two inaugural galas without incident, made its official coat count available.

Of the 16,000 coats checked for the two balls held there Monday night, "only 0.6 percent -- about 60 coats -- remained unclaimed" by 2 a.m. Tuesday, according to Michael Rogers, deputy general manager.

The center, which contracts with King Enterprises for its coat check services, is trying to return the coats.

Rogers said that of the 36 ball guests who came in yesterday, 34 left with their coats. About 26 coats -- men's and women's fur, cloth, leather and cashmere wraps -- were still hanging on four racks late yesterday.

And if U.S. Army Capt. Lawrence Charles Mohr Jr. kept his claim ticket -- No. 245 -- he can pick up his hat, the one with his name clearly labeled inside, any time.

Rogers said the center has accommodated larger crowds but not under the same tight security restrictions required whenever a president plans to drop by. President Reagan had come and gone by 9:30 p.m., and Vice President Bush's departure around midnight set off a mass exodus.

The coats had been checked at the front entrance, assigned pink, green, blue or yellow claim checks and later carted off to color-coordinated rooms for storage. "Runners" were ready to fetch the garments when called.

But the system broke down, Rogers said, when ball guests became impatient and began going directly to the coat check rooms to search for their coats.

"There were people in the hall who appeared to be in an unusually festive mood," Rogers said.

A coat check attendant put it less politely: "They were drunk."

"Some tried to give assistance to our personnel," Rogers said.

But attendants said a small group of guests elbowed employes, turned over a table and charged into the coatrooms, knocking garments and claim checks to the floor. One supervisor said she was punched in the face by an angry coat searcher, though no charges were filed.

Krupo and another witness said the attendants, in fear and exasperation, eventually walked off the job or hid in a back room. The attendants deny this.

Bill Bushelle, a ball guest from Mount Vernon, said he checked three coats and got back two, including a fur, after an hour's wait. He finally got the two coats himself because a friend was circling the block, waiting for him. He was back yesterday, hunting unsuccessfully for his coat. "The attendants were trying to be helpful," he said. "But they were overwhelmed."