DALLAS (AP) _ A local political tradition has broken down and no single candidate enjoys the collective blessing of the business community for the non-partisan mayoral election Saturday.

''There is no anointed candidate as there have been in the past. The oligarchy's dead,'' said Dallas County Republican Party Chairman Tom James.

Four millionaires lead a pack of nine vying to succeed A. Starke Taylor, who decided not to seek a third term as mayor of the nation's seventh-largest city. Each of the top four claims support from among Dallas' corporate elite, and they are expected to spend a combined total of $3 million.

In the past, political observers say, tightly knit organizations led by business leaders were able to pick mayors, using their financial clout to secure the election. But this year a consensus is lacking.

''There is a continuing breakdown of what was a monolithic system,'' said Sandy Kress, chairman of the Dallas County Democratic Party. ''What you have is a fragmentation of the big-moneyed interests, and what you're finding is the city is becoming more diverse.''

Both party leaders welcomed the trend.

The four main contenders are businessman Jim Buerger, 46; former Republican Rep. Jim Collins, 70; former Dallas County Republican Chairman Fred Meyer, 59; and City Councilwoman Annette Strauss, 63.

Both Buerger and Collins said they consider Mrs. Strauss the front-runner; she and Meyer declined to make projections. But all four top candidates said they expect to be involved in an April 18 run-off, because no one is expected to garner 50 percent of the vote Saturday.

Mrs. Strauss is running on her four years of city council experience, plus nine years of service on city-related boards. She would be Dallas' first woman mayor if she wins.

Crime, housing and transportation are her top priorities, along with economic development in the face of a statewide economic downturn.

She agrees with other candidates in lamenting that partisanship has entered the election more than in past years in a city where candidates generally have eschewed party labels.

Mrs. Strauss said she is not running as a partisan candidate, but cannot avoid association with the Democratic establishment - her brother-in-law is Robert Strauss, former chairman of the Democratic National Committee.

Another candidate who bears a party label by association is former county GOP chairman Meyer, who was endorsed by incumbent Taylor.

Meyer, who resigned as president of Dallas-based Tyler Corp. to take his first shot at public office, said crime and the local economy are the main issues.

''Dallas is not used to having a rough time,'' Meyer said, pointing out that the city expects a budget deficit this year because of problems in the oil, banking and real estate industries.

''It's a strange election,'' said Collins, a Republican who served 16 years in the U.S. House before running unsuccessfully in 1982 for the Senate. ''I've lived in Dallas most of my life and this is the most aggressive campaign I've ever seen.''

Collins' focus is crime and taxes. He labels Mrs. Strauss a liberal in contrast to his staunch conservatism and comments: ''We have never had a liberal mayor in Dallas.''

It is the first political race for Buerger, who, by outspending all the other candidates at $750,000 by mid-March, has shot into the spotlight from previous obscurity.

Buerger, chairman of the board of Travel Host Inc., a publishing company, is the only political independent among the front runners.

He promises to focus on crime in this city which has one of the highest crime rates in the nation. His next priority is the economy.

Also running are law firm investigator Marvin Crenshaw, 41; factory worker Roni Lerouge, 26, a member of the Socialist Workers Party; businessman Billy Jack Ludwig, 57; assistant bookstore director Marvin Steakley, 61; and Gardell Morehead, 36, a Lyndon LaRouche supporter who has run unsuccessfully for mayor and for Congress.