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It was a common gesture, really, a smile and a wave from the driver of one car to the passenger in another as both slid up the entrance ramp to the Eisenhower Expressway, heading into the city in the middle of the afternoon.

But the passenger in the back seat of the dark blue Lincoln quickly leaned forward and, smiling broadly, waved back at the young black woman who had waved almost reflexively when she recognized the man in the car next to hers.

”Did you see that?” the passenger asked a companion in the sedan`s back seat.

”The last time, it might have been one of these,” he said, extending the middle finger of his left hand and jerking it upwards in the time-honored gesture of challenge and disdain. ”Things are different out there this time. You can feel it.”

The passenger was State`s Atty. Richard M. Daley and ”last time” was in the heated and racially tense Democratic mayoral primary election of 1983, when the son of the late Mayor Richard J. Daley stumbled on the steps of destiny in his attempt to take over the 5th floor office in City Hall his father occupied until he died in December, 1976.

The ”last time,” a sometimes tongue-tied younger Daley finished third in a three-candidate race. He was often rattled during campaign appearances by Harold Washington`s talent for delivering a burgeoning potpourri of rhetoric and the razor-sharp slashing style of Mayor Jane Byrne.

But that was ”last time.” This time, life looks good for Richard M. Daley, looser, relaxed, on the campaign trail.

Although he started his mayoral campaign with the televised announcement that he was not the best speaker in Chicago, he has shown in the subsequent weeks that he is not the worst either.

Campaign money seems plentiful, so much so that Daley television commercials are airing almost daily, even though the Feb. 28 Democratic primary election is still weeks away. The candidate has surrounded himself with proven professionals in the election business and maintained the vestiges of his much quieter re-election campaign for state`s attorney in last November`s general election.

And nearly every poll shows him with a commanding lead over Mayor Eugene Sawyer, Ald. Lawrence Bloom (5th) and other peripheral candidates in the primary race.

Life is good this time on the campaign trail, and so it was one day last week when his driver and car (furnished by the County of Cook because of his position as state`s attorney) picked him up at his Bridgeport neighborhood home, just a scant block from the family home where he was raised.

The first stop was a private one, meeting with friends, strategists and donors at a private club in downtown Chicago, and the second one was also private and ”off the record,”-a breakfast huddle with executives and producers of WLS-TV in an 11th floor conference room in the station`s building at State and Lake Streets.

Shortly after 9 a.m., Daley and a few aides walked the three short blocks to the Daley Center, the imposing building across the street from the City Hall-County Building that was named for his father. As state`s attorney, he divides his time between here and offices in the Criminal Courts Building on the West Side.

It has been said that one of the best ways to check the direction of the wind, political or otherwise, is to look at a weather vane. In City Hall, that weather vane often is Ald. Dick Mell (33d), the affable, white-haired gent who became an international symbol of Chicago when he was photographed standing on his desk in the City Council chambers shouting for attention the night Sawyer was chosen to succeed Washington in December, 1987.

Daley was not surprised to see Mell in his outer office, and when Mell asks, ”Gotta minute?” Daley replied, ”Sure, come on in.”

It is in his Daley Center office where he holds political court these days, and if he insists on running on his own record, a visit to his inner sanctum leaves no doubt from whence his political background sprang. The walls, the end tables and the state`s attorney`s personal desk are covered with pictures and trophies of Richard J. Daley, the man who became mayor when the son was 13 and remained mayor until he died 21 years later.

Back in the Lincoln, shortly before noon, heading for a speech to a group of hospital administrators, Daley looks out the car window on the Eisenhower and sees the tall buildings of the University of Illinois-Chicago, surrounded by new apartment buildings and hospital structures.

”You know, when people ask me what the greatest thing my dad ever did, I say it was the University of Illinois here. Without that, this would have been nothing,” he says, apparently vindicating the uproar created at the time when the senior Daley oversaw the carving out of old-time ethnic neighborhoods to create the Near West Side university campus.

Usually in public appearances, Daley doesn`t mention his legendary father; he doesn`t have to. Others do it for him, as the campaign day progresses.

Later in the afternoon, Daley settles down on an artificial leather couch in the lounge of a Chicago Housing Authority senior citizens center in the West Side Austin neighborhood, surrounded by a group of elderly black residents to talk about health and housing problems.

”Your father was the first man I ever voted for,” offers a 74-year-old woman, the mother of 18, and Daley lowers his head, smiles and says, ”Thank you.”

On the way out, Daley, for the second time of the day, stops and is surrounded by television crews and reporters for what is indelicately self-described by them as a ”gang bang,” an unscheduled opportunity for the press to ask the candidate about anything. Avis LaVelle, the former WGN radio reporter hired to serve as Daley`s press secretary and most visible spokesperson, mother-hens Daley in and out of the media cluster after all of the questions have been asked.

The remainder of the afternoon is spent preparing for an early evening forum for mayoral candidates sponsored by the YWCA of Metropolitan Chicago, the Illinois Women`s Agenda and the National Organization For Women (NOW), a group that, it could be supposed, might have been hostile to the late Mayor Daley, Democratic by tradition but conservative by act.

That preparation includes the answer for the expected ”A question,” a request for the views on abortion from the Catholic candidate.

The response is polite when he is introduced and during his 10-minute presentation, a neat and generalized summing up of why he should be mayor, with a few facts about his affirmative action record as state`s attorney thrown in.

Then comes the ”A question,” couched in the form of ”What is your position on choice?” He`s ready for it.

”To be frank, I`m against it,” he says. ”But I`m state`s attorney, and I follow the law. I think it should be something between a doctor and his patient, just like a lawyer-client privilege.”

”This is the 1990s,” he says, always his father`s son. ”We cannot close our eyes or run in the closet.”

The crowd applauds politely; it neither cheers nor jeers, a victory of sorts for a candidate who is avidly seeking the so-called Lakefront Liberal support some professional women in the group represent.

And another day is done on the campaign trail, where, for the moment, at least, life for Richard M. Daley is good.