The bands will bicker back and forth, the teams will do worse than that, and many bleary-eyed alum will think, "Oh, to be in uniform when Notre Dame hosts Southern Cal in the annual classic today." The series that dates back to 1926 has involved 19 national champions and 10 Heisman Trophy winners, and never mind the recent lessening of national significance -- both teams are working on that.

The incurably romantic rivalry is in its 59th renewal, which is exactly the right word for this season's nationally televised meeting at Notre Dame Stadium (WUSA-TV-9, 1:30 p.m.). Tenth-ranked Notre Dame (4-1) is experiencing a happy regeneration under Coach Lou Holtz, while USC's Larry Smith is attempting to bring some fight back to the Trojans (4-2).

Both teams are trying to recover from surprising losses, the Irish bemoaning an upset by Pitt two weeks ago, the Trojans frustrated by an opening loss to Michigan State and then a disappointing defeat two weeks ago to Oregon. But both are on the upswing coming into today's game, which could very well be a season- and postseason-maker. Twelve bowl scouts will be present.

"They're very, very explosive," Holtz said worriedly of Southern Cal. "In the last few weeks no one has even slowed them down." Smith replies to Holtz's moaning assessment: "It's made of sugar, it melts in your mouth."

There have been only six occasions when both teams came into the game unranked, and two came in the last five years: in 1983 and 1985 as the Irish went awry under former coach Gerry Faust and the Trojans meandered on the verge of mediocrity under Ted Tollner. Whether the game is returning to one of actual meaning will be determined in large part by whether Smith can mount the sort of turnaround with the Trojans that Holtz has with the Irish.Tough Times for Trojans

Southern Cal still throws out its chest and the band still prances in its high-stepping way, but the football team has somehow lacked authority, as last year's 7-5 mark indicated. They haven't been to the Rose Bowl since the 1984 season, followed by trips to the Aloha and Citrus, both losses.

The Trojans also lost four consecutive games to the Fighting Irish under Tollner, including last year's 38-37 decision after leading, 20-7, at halftime, one reason for his firing. They are weary of slumming.

"We've had our ups and we've had our downs, and I'm tired of the downs," all-America linebacker Marcus Cotton said.

The Trojans remain an enigma, ranked sixth in the country offensively but nowhere in the top 20 defensively. However, between the losses came three straight victories and they got a fourth last week with a 37-23 upset of Washington. Among Smith's first moves was to institute a tougher conditioning program, remedy some disorganization, and take a firmer tone in general than the soft-spoken, well-liked Tollner.

"It's his way or no way," Cotton said.

Last week, when the Trojans were penalized 13 times against Washington, Smith laid into his players, then told his assistants he wants to be informed if anyone is seen misbehaving.

"If we get any more of those, that person, no matter who it is, will be out of the game," Smith said. "I don't care who it is. Two things I can't stand are showboating and unsportsmanlike conduct. I've had enough of it."Return of the Run

Smith's other major change has been to proclaim a return to the great Trojans running tradition, an ever-present spectre in USC's Heritage Hall, where Heismans belonging to Mike Garrett, O.J. Simpson, Charles White and Marcus Allen are housed. But "Student Body Left" had suffered a decline in recent seasons, with no predominant tailbacks.

The Trojans finally have one in junior Steve Webster, who has carried 133 times for 604 yards and four touchdowns in five games, after missing the opener with a sprained ankle. Actually, he is one of three primary revolving backs, alternating at times with freshmen Scott Lockwood and Ricky Ervins.

The Trojans use a multiple offense, running out of everything from the I, to split backs, to single back, and the result is that they are the sixth-ranked overall offense in the country, averaging 454.7 yards. That also is due in part to superbly athletic junior quarterback Rodney Peete, who is fourth in the nation in passing efficiency and ninth in total offense, averaging 241 yards a game.

"It's a very definite change from the last couple of years," Peete said. "When Coach Smith came here he said he was going to bring back the SC run, and that's what we've done. That's the way it was when I was growing up. It's a classic USC game, with the offensive line that dominates. When you talk to alum, they all want that tailback to carry the ball 40 times."

But they have not by any means ignored the pass. Peete has almost as deep a group of receivers as he does a backfield, and has completed 95 of 152 passes for 1,363 yards and 10 touchdowns. He throws to split end Ken Henry (15 catches for 263 yards), flanker Randy Tanner (15 catches for 253 yards, three touchdowns) and split end Erik Affholter (19 catches for 294 yards, three touchdowns). A moonlighter as starting shortstop on the USC baseball team, he is a dangerous scrambler as well as passer, who has been sacked just twice this season and has rushed for 86 yards.

Peete has known Smith since he was 7 years old. His father Willie Peete, now an assistant with the Green Bay Packers, was a longtime assistant at Arizona, first as a colleague of Smith's and then under him from 1980 to 1983. Peete chose Southern Cal instead of Arizona, he said, because, "It appealed to my mind when I was young. That white horse running around, and that band marching down and taking over the field."

That appealed to Smith, 47, too, which is how he wound up with the Trojans after seven years at Arizona. While there he pulled off a 16-13 upset at Notre Dame Stadium in 1980.

But this is the first time he goes there with Southern Cal.

"If you let the aura get to you, you'll spend a lot of time in awe and none in preparation," Smith said. "It's a great rivalry, a great tradition, but you can't get wrapped up in it. You don't play the aura, you play Notre Dame."