A surge in the Chicago black vote bodes well for the Democratic Party in '84; meanwhile, Mayor-elect Washington promises to unite the city and end political patronage; and in Philadelphia, Democratic mayoral primary candidates try to keep the issue of race subdued.
Leaders of both national political parties are relieved that Chicago's bitter and divisive mayoral campaign lies behind them.
Neither the Democrats nor the Republicans were entirely happy with their candidates or with the potential ramifications for 1984. They definitely were disturbed by the racial polarization that surfaced in the city.
As it is, Democrat Rep. Harold Washington's narrow victory over Republican Bernard E. Epton, followed by appeals for community unity from all factions, yields these conclusions:
* The basic Democratic coalition of blacks, Hispanics, white liberals, and unions came together sufficiently to pull it out for Mr. Washington, the black candidate with a mixed legal record.
All these groups are working toward having a greater impact on voting in November 1984. The National Coalition on Black Voter Participation reports that black voter registration in the United States rose from 60 percent in 1980 to nearly 65 percent in 1982. The coalition has plans for campaigns in 55 cities besides Chicago for '84 and in 22 states crucial to Democrats' prospects. The victory by a black in the Chicago mayoralty - after black registration was remarkably boosted from 50 percent to 75 percent in two years - could spur black registration drives nationally. It weakens the argument that a black presidential candidate is needed to encourage further black registration, says Gracia Hillman, the coalition's executive director.
* The Republican Party made a far better showing in the Chicago contest than it has there in years. It can point to tens of thousands of names on its computer lists - an improved Chicago base for the '84 reelection campaign of Sen. Charles H. Percy (R) of Illinois. Still, the election underscored the GOP's image among blacks as the white voter's party.
''Regrettably and unfortunately, but also truly, the (Republican) Party is at an all-time low among blacks today,'' says William Greener, Republican National Committee spokesman. The Chicago experience ''doesn't make the task any easier to make the gains with blacks the Republicans want.''
* Republicans and Democrats alike hope to see Chicago follow the pattern set by cities in Michigan and other states, where black mayors have forged a working coalition with moderate Republican governors. This has offset political hostility in white suburbs during crucial legislative battles. Detroit's black mayor, Coleman Young, worked effectively with former Gov. William Milliken (R) on jobs and tax programs helpful to the city. The links to Chicago's City Hall already established by Illinois GOP Gov. James R. Thompson could work to his and to Mr. Washington's benefit.
Looked at more locally, Chicago's election of Washington does not ensure that the city's leadership succession following the 1976 passing of ''boss'' Mayor Richard J. Daley has been settled. Recent officeholders Michael Bilandic and Jane Byrne were regarded as interim mayors. Washington has a chance to lead the city into a new political era.
Despite the emotional pitch of the campaign, Chicago endured its first serious election bid by a black mayoral candidate reasonably well, compared with shifts from white to black leadership in other major cities.
''For all the talk about the campaign - and it was tough, no doubt about that - Washington still got 17 percent or 18 percent of the white vote,'' says political strategist Paul Maslin, vice-president of Patrick Caddell's Democratic consulting firm. ''That's better than almost any of the other black mayoral candidates in their first general elections.''
To Democratic analysts, President Reagan's leadership in Washington will be a far greater catalyst for political activism in 1984 among blacks than Harold Washington's win in Chicago will be among whites.
''The registration of blacks nationally is not occurring in a vacuum,'' says Maslin. ''That man with the likable smile in the White House is generating it. It is happening everywhere - Boston, Philadelphia.''
''The Republican Party is just gone now with blacks,'' he adds. ''(Senator) Percy got black votes in '78. So did (Governor) Thompson earlier. But Thompson got no black votes in '82. And Percy won't get any in 1984.''
Race today is a potent factor in American voting. In the last congressional elections, those identifying themselves as Afro-American voted 90 percent Democratic, according to ABC News exit polls. Hispanics voted 72 percent Democratic. Whites voted 53 percent Democratic, 44 percent Republican.
Reagan shows almost no support among black voters. In a February Penn & Schoen survey, 71 percent of blacks said they would vote against Reagan in 1984; 23 percent said they would consider voting for someone else; and only 1 percent said they would definitely support Reagan.
Earlier in this century, the GOP had an edge among blacks as a legacy of Abraham Lincoln and the Civil War. In the 1920s the GOP's margin was 5 or 6 to 3 over the Democrats, says Everett C. Ladd, a University of Connecticut political scientist. After the Great Depression, the Democrats gradually built strength among blacks until by 1960 they held a 2 to 1 margin.
The GOP's ''Southern strategy'' in 1964, which appealed to angry white voters , cemented the trend, Mr. Ladd says. Black support, 30 percent for Richard Nixon in 1960, dropped to 2 or 3 percent for Barry Goldwater in '64, and has stayed that way ever since.