The four Salt Lake City mayoral hopefuls were all smiles at the University of Utah Thursday. But it may be last such cordial meeting between Deedee Corradini, Mike Zuhl, Dave Buhler and Dave Jones - who all seek to replace Salt Lake City Mayor Palmer DePaulis.

Corradini is a businesswoman, Zuhl is DePaulis' chief of staff, Jones is a small businessman and state legislator and Buhler is a former aide to Gov. Norm Bangerter who now heads the state Department of Commerce.The four discussed why they should be mayor in an appearance at the Hinckley Institute of Politics, co-sponsored by college Democrats.

Depaulis decided not to seek another four-year term this year, and is expected to run for governor in 1992. Institute director Ted Wilson said the 1991 mayoral race offers an open seat for the first time since 1971. "That is probably why we already have such a good, qualified field of candidates," said Wilson, who served as Salt Lake mayor before DePaulis.

Salt Lake City council and mayoral races are officially non-partisan; that is, a candidate's political affiliation isn't mentioned on the ballot. But traditionally there's been a Democratic candidate facing a Republican candidate in the final election.

Corradini is a Democrat, working on the staffs of former Gov. Calvin Rampton and U.S. Rep. Wayne Owens before opening a governmental consulting firm 14 years ago.

Zuhl is a Democrat, serving in former Gov. Scott M. Matheson' administration as state budget director.

Jones is a Democratic House member representing the east-central part of Salt Lake City in the Legislature.

Buhler is the only Republican so far to announce, but the filing deadline isn't until August. He worked on Sen. Orrin Hatch's Salt Lake staff, then entered state government with Bangerter in 1984. After managing Bangerter's successful 1988 re-election, Buhler was named executive director of commerce.

While the four spoke mostly about themselves and their qualifications to be mayor, hints of tougher statements to come peeped through.

Buhler said he doesn't represent the City Hall gang (referring to Zuhl) nor the corporate elite (referring to Corradini). Corradini said she, at age 47, is the senior member of the group (referring to the relative youth of Zuhl and Buhler). Jones said he won't run a slick, media campaign based on telemarketing (a reference to Zuhl, Buhler and Corradini, all who will likely raise more money than he).

Buhler challenged the other three to "at least 20" debates from now until the Oct. 8 primary election. Zuhl accepted, "I'll meet you anywhere, any time. I know the issues of the city better than anyone." But neither Jones nor Corradini immediately accepted Buhler's challenge.

All said they are serious about the campaign, plan to win and have specific agendas to deal with the city's problems - which include a dwindling resident population, aging and deteriorating housing stock, crime and providing high quality services during a time of shrinking municipal budgets.