Woody Hayes, an old military man whose temper tantrums were as legendary as his success on the football field, was fired today after 28 years as head coach at Ohio State University.

The dismissal of Hayes, 65, whose 33-year coaching record of 238 wins, 72 losses and 10 ties ranks him fourth in victories among past and present college coaches came with stunning swiftness, just hours after he punched a Clemson player, provoking a bench clearing melee in the closing minutes of Ohio State's 17-15 loss to Clemson in the Gator Bowl here Friday night.

The incident occured with two minutes to play when Clemson middle guard Charlie Bauman intercepted an Ohio State pass with the Buckeyes driving for what could have been the winning points.

Bauman, who intercepted Art Schlicter's pass at the Clemson 27, returned the ball to midfield and was pushed into the sideline area occupied by Hayes and the Buckeye players.

Hayes grabbed the startled player and swung at him.

At 7:30 this morning, Ohio State Athletic Director Hugh Hindman, after an early morning meeting with Harold Enarson, university president, notified Hayes he was through.

"It was the toughest decision I will ever have to make," Hindman said in a statement. He said Hayes' actions against Bauman led to the coach's firing.

An intractable, conservative man who preached a gospel of family, country, discipline and football with the fervor of a fire-and-brimstone pastor, Hayes had come under increasing attack from critics of his old-fashioned philosophy and coaching methods, which lately seemed to yield diminishing returns on the field.

Hayes built Ohio State into an awesome gridiron tradition after taking over in 1951, but had not beaten arch-rival Michigan in four years nor gone to the Rose Bowl as the Big Ten champion since 1976. Ohio state's 7-4-1 record this season was its worst since 1967.

Hayes' unbecoming conduct Friday night was the latest in a series of widely publicized on-the-field outbursts and was primarily responsible for his ouster.

"I think that's obvious," said Hindman, who, with Enarson, apparently decided after the game that Hayes had become an embarrassment to the school to which he had brought so much sporting glory.

Hindman informed Hayes of the decision this morning. Hayes flew back to Columbus with his team on a charter flight, and Hindman made the announcement of his dismissal at a hastily called news conference in his hotel room while the team was in the air.

Flushed and with tears in his eyes, Hindman read a terse statement: "Coach Hayes has been relieved of his duties as head coach at Ohio State University. This decision has the full support of the president of the university."

Hindman said his job as messenger of doom had been extremely difficult.

"I've known Woody since 1949.I played for him, and coached under him for seven years," said Hindman, a former offensive guard who began his career as Hayes' offensive line coach.

At a news conference in Pittsburgh later, Hindman said he met with Hayes immediately after the game and told the coach "to expect the worst." He said he fired Hayes after the coach refused to resign, saying, according to Hindman, "It'll make it too easy for you. You better go ahead and fire me."

He said the search for a successor would begin Monday. Speculation immediately centered on Arkansas' Lou Holtz, who began his coaching career under Hayes. Holtz reportedly told a Little Rock radio station this afternoon that he was not interested in the Ohio State job.

While reports of Hayes's dismissal were rampant on the team plane that returned to Columbus this merning, Hayes waited until the chartered jet was on the ground before telling the players he was no longer their coach.

Hayes then hurried off the plane ahead of the players, avoided a horde of waiting reporters and sped away in a police cruiser.

Earlier, he telephoned Columbus Dispatch sports editor Paul Hornung and said he had resigned.

Hayes' dismissal caused widespread shock. "I'm sure the players didn't know anything about it when they left," said All-America linebacker Tom Cousineau, one of two Ohio State players who remained in Jacksonville because they are headed for an allstar game in Hawaii next weekend.

"I'm just stunned. The man is an institution. He's been a winner for 28 years. He is Ohio State football. So how do you fire somebody like that?

"I can't condone what he did," Cousineau continued, "but it's a shame because Coach Hayes is a great man and a terrific coach. If I had it to do over, I'd play for him again, and so would most of the other guys."

A crowd of 72,011 and a national television audience were startled and outraged when the volatile Hayes grabbed and punched Bauman after his interception Friday.

After Bauman was knocked out of bounds, he held the ball aloft in an apparent taunting gesture. The stocky Hayes rushed at him, grabbed him around the back of the neck, spun him around and punched him, all the while screaming obscenities.

This touched off a free-for-all as both teams rushed on the field and began shoving. Several fights broke out. Clemson defensive back Willie Underwood was felled by a punch to the midsection, and Ohio State linebacker Leon Ellison suffered a possible broken jaw.

In the confusion, Hayes struck at least two of his own players. He jumped up and down furiously, shrieking in rage, and seemed to want to fight anyone in sight. One of the Ohio State players Hayes struck, lineman Ken Fritz, said: "It didn't bother me, 'cause I just take things as he gives them."

When order was restored, Ohio State was assessed a 15-yard penalty for unsportsmanlike conduct. Hayes-who suffered a mile heart attack in June 1974 but did not let that mellow him-continued to rant at the officials and was docked with another unsportsmanlike conduct penalty after the next play.

"After I was tackled, there was so much excitement, I don't know what happened," Clemson's Bauman said.

Obviously upset, he added, "I don't think he [Hayes] should be out there coachint. I know Woody has been known to do things like that."

"It was an ugly way to end a game and a season," said Kelton Dansler, another star OSU linebacker, who said he admires Hayes but had witnessed an erosion in respect for the coach during his four years at Ohio State.

"I guess this typified our whole season, all the frustration," added Dansler, who, like many of histeammates, was exasperated as preseason predictions of a Big Ten title and Rose Bowl trip for the Buckeyes fizzled.

"It's degrading, ending up fighting like that," he said. "It's a disgrace to the game, the schools and everybody involved."

"I didn't see what happened and I expected Coach Hayes to single out whoever started the ruckus in the dressing room after the game, because fighting on the field is something he has always been against. But he didn't say anything. That makes me think maybe he did start it. The people who watched on TV said so.

"I think he's a great man who pushed a little too hard and tried to hang on a little too long."

Hayes' snits and outbursts on the sidelines have become a familiar spectacle, but several violent episodes embroiled him in repeated controversies during the last decade of his career:

On Nov. 21, 1971, he ran onto the field to protest a call late in Michigan's 10-7 victory over Ohio State, incurred an unsportsmanlike-conduct penalty and had to be restrained by players and assistant coaches from attacking an official. Back on the sideline he broke a yard marker over his knee and shredded a first-down marker.

On Jan. 1, 1973, before Southern Cal thrashed OSU, 42-17, in the Rose Bowl, Hayes pushed a camera into the face of a Los Angeles Times photographer who was trying to take a portrait of the head coach framed through the legs of one of his assistants. "That'll take care of you, you son-of-a-bitch," Hayes reportedly told the cameraman, who pressed charges of misdemeanor battery, but later dropped them.

On Nov. 19, 1977, after an Ohio State fumble killed a late drive during a 14-6 loss to Michigan, Hayes took a swing at ABC cameraman Michael Freidman on the sideline. He was placed on one year's probation by the Big Ten.

Hayes frequently has stormed out of news conferences, snarling at the reporters he recently characterized as "nosy pipsqueaks" for their probing questions after OSU defeats. The most recent tirade and abrupt departure came Nov. 25 after a 14-3 loss to Michigan.

A native of Clifton, Ohio, Wayne Woodrow Hayes got his first college coaching job in 1946 at his alma mater, Denison University in Granville, Ohio, after five years in the Navy.

He coached there for three years, then at Miami of Ohio for two before going to Ohio State. His 28-year record at OSU was 205-61-10. He won or tied for 13 Big Ten titles, won three national championships and was voted college coach of the year twice-1957 and 1975.

His overall record places him fourth in career victories, behind Amos Alonzo Stagg, Glenn (Pop) Warner, and Paul (Bear) Bryant. Bryant-whose Alabama team thrashed Ohio State, 35-6, in last year's Sugar Bowl-is the only active coach with more college victories.The Sugar Bowl was their first confrontation, and it left Hayes punching the goal posts in the Louisiana Superdome in anger.

Hayes is a man of absolutes for whom the world is clearly delineated into "winners" and "no-accounts." His supreme and outspoken confidence in old values, and his dogmatic nature, made him both beloved and despised.

Dansler, who said he was embarrassed for Hayes when the coach threw his tantrums, said he would remember Hayes "many different ways because he was many different people. Off the field he was the softest, gentlest man you could ever meet. On it he was a different person."

A few minutes after, Dansler gave an impression of Hayes that many other players undoubtedly would echo: "He's a man that you could compare to no other. He does his thing different from anybody else, and if it please him he's going to do it that way, regardless of what anybody else says.

". . . But 28 years is a long time to be a coach at one school. All empires, like the one Woody built, eventually crumble from within . . . Maybe time passed him by. Everybody says players have to realize they can't spend their whole life with football. I think it's the same with coaches. They don't age any more gracefully than players." CAPTION: Picture 1, OSU player, aide restrain Woody Hayes after he hit Clemson player. UPI; Picture 2, WOODY HAYES . . . 28 years as head coach at Ohio State