An aura of deja vu pervades Chicago's mayoral campaign, inducing a sense of serenity among a populace that only a few months ago expected political turmoil, if not outright anarchy, in the wake of Richard J. Daley's death.

To be sure, Daley's name is absent from the list of candidates for the first time in 22 years, and the race undeniably lacks the robust, boisterous Irish enthusiasm that Daley brought to his five capaigns.

But all the same, there are similarities, beginning with the most familiar the outcome of the Tuesday primary is inevitable.

In a city where Republicans have trouble getting together two tables of bridge for a fund-raiser, the winner of the Democratic primary also wins the right to sit on the fifth floor of City Hall. and the winner of the Democratic primary will be -- unless the sun rises in the west on primary day --training and a bookkeeper by appearance.

Until Mayor Daley tapped him in 1969 to become alderman of the awesomely powerful 11th ward -- Daley's home ward -- Bilandic was just another discreet insider. With the support of the bosses of the Cook County Democratic Central Committee, Bilandic was elected Dec. 28 by the City Council to act as interim mayor after Daley's death, and in so doing, the council presented Bilandic with the keys to the machinery of the regular Democratic organization.

And ever since he ask been to persuade voters that although the name has changed nothing is really different.

Bilandic himself strives mightily to project the image that Chicagoans are simple reliving a previous election. He has, for instance, mastered in 14 weeks as acting mayor Daley's distinctive speech: Bilandic can talk without moving his lips. That is no mean feat and it has reinforced the sense of continuity among voters that Bilandic is indeed the rightful heir to Daley's fifth-floor office.

What Bilandic says and doesn't say also is remarkably familiar. He offers no new programs, plans or agendas for the future and neither did Daley. What Bilandic does do is talk about Chicago's secure financial health and its high bond rating. He talks about his successful forays to Washington whence he returns with bags of federal funds. And he cites his short but successful record in mediating labor disputes -- which are securely in the Daley tradition.

What Bilandic is selling -- and selling successfully -- is the status quo. Invoking his favorite metaphor he tells his campaign-trail audiences, "The ship of Chicago is on an even course. It has survived the stormy waters . . . it remains on a steady keel," and under his watchful eye it did not wander "into unchartered waters" after Daley's death.

For all the similarities, however, Bilandic is a meager reflection of the jowly enthusiasm that best characterized Dick Daley. Where Daley, his florid face suffused with the sheer delight of campaigning, could bring the party faithful screaming to their feet and streaming to the polls. Blandic leaves them snoozing in their chairs. Quiet, studious, ascetic and meticulously dressed in three-piece suits, Bilandic aw-shucks his way through speech after speech: "I'm just a local boy who is not a politician. I don't understand that sort of thing."

Then he hits them with a few "ship of chicago" metaphors and bows out to polite, friendly applause.

In the background are Bilandic's five Democratic challengers choking with rage because they know -- no matter how uninspiring bilandic may be as a candidate -- that come April 19 the relentless Democratic machine will turn out enough votes to make bilandic the mayor of Chicago.

Bilandic's most formidable foe is Alderman Roman Pucinski, 57, a heretofore dependable cog in the party's machinery, having served 14 years in Congress and four in the city Council.

Pucinski believed Bilandic when he became acting chief executive and declared, "I am not a candidate for mayor." Later when Bilandic succumbed to a "spontaneous" draft by the party's 50 ward committeemen who write the slate of candidates for all city offices, Pucinski still hadn't come around. Pucinski got one vote from the slatemakers -- his own.

But he persisted. Now he finds that from among the 84 once-loyal precinct captains in his ward, at least 30 have defected to Bilandic. His supporters --other Eastern European ethnic blocs --broken, their cars demolished and receive unexpected frequent visits from city inspectors who find various and sundry building code violations in their homes and offices.

A special federal grand jury has been convened to investigate Pucinski's charges of terrorism and harassment, but if anything comes of it, it will be too late to do Pucinski any good at the polls.

For his part Bilandic says, "I am shocked and surprised to hear [Pucinski] whining and crying" about harassment, and the acting mayor suggested the entire situation may have been perpetrated by Pucinski supporters to curry sympathy.

The acting mayor's other challengers include former State's Attorney Edward Hanrahan, 55, who has won only one of his last four races for any office and finished last in the 1975 mayoral primary; Harold Washington, 54, a black state senator who has served time for failing to file federal income tax returns, Ellis Reid, 43, a black attorney and former Democratic precinct captain who campaigns almost exclusively in the black ghetto, and Anthony R. Martin-Trigona, 32, a self-styled and wealthy consumer advocate.

The four Republicans are even less threatening. They are led by Dennis Block, the lone Republican in the 50-member City Council who was pressed into reluctant service when no one else could be found; A. A. Sammy Rayner Jr., former alderman bereit of any organization support; Frank Ranallo, a retired locomotive engineer who has declared he wouldn't permit a black to live next door to him, and George Manning, a pest exterminator.

Given that kind of opposition, the talk among voters and political experts here centers on the margin of Bilandic's victory, which was precisely the topic of conversation during Daley's terms of office. Little wonder, then, that Chicagoans feel they've been here before.