That’s the situation at Apple Computer. No doubt: the troubled maker of Macs has shown some world-class moves. At Macworld, it rallied the faithful and cleaned house with an all-star board. Larry Ellison, software’s second leading billionaire. Steve Jobs. Jerry York, the turnaround king from Chrysler and IBM. And on the bench, shepherding his new $150 million investment in Apple: William H. Gates, probably the smartest and hardest techno-player of them all. There’s just one problem: these strong-willed, charismatic tycoons rarely agree on anything. They’ve devoted their lives to beating each other up. So now they’re supposed to make happy-happy at Apple?

Jostling one-on-one with these guys will be bruising. But someone has to lead Team Apple. The question around Silicon Valley is, who? Until last week Jobs himself was rumored to become Apple’s new chief executive or chairman. But he has held back, and Mac watchers are scribbling lists of new candidates. Among those most frequently mentioned is Bill Campbell, 56, chief executive of the software maker Intuit. Founder of Claris Corp. and a former executive vice president of Apple, Campbell also joined Apple’s board last week. Respected for his technology expertise, gruff but calm demeanor and ““win-win’’ management style (Campbell once coached football at Columbia University), he is widely described as a model of the sort of chief executive Apple needs - confident and knowledgeable enough to go nose to nose with Jobs or Ellison, diplomatic enough to smooth conflicts within the board. But would he take the job, if offered? No, Campbell tells NEWSWEEK: ““I have a good job at Intuit, and that’s where I’m staying.''

Other names also come up. Joel Kocher, a former senior executive of Dell Computer and the president of Power Computing, the leading Mac cloner, recently met with Jobs, according to trade reports. James Cannavino, who recently resigned as head of Perot Data Systems, has been mentioned. So has Del Yocam, chief of Borland International, another software company. Another pos- sibility, Eric Benhamou, head of 3Com Corp., has already declined a board seat. Now Jobs appears to be trying to interest George Fisher, chairman of Eastman Kodak, seemingly without success. ““Why would George want to run Apple?’’ asks Geoffrey Champion, managing director of Heidrick & Struggles, an executive-search firm in Menlo Park. A top CEO like Fisher, who rebuilt Motorola and is rumored to be in line for the top job at AT&T, won’t lightly risk his career on a failing Apple, Champion explains. ““It will be a tough recruitment.''

Here is Apple’s dilemma. It wants a ““world class’’ chief executive. But a strong chief who can hold his own against Jobs, Ellison & Co. may look at Apple and conclude the challenge isn’t worth the heat - or the frustration of being second-guessed by directors who assume they know more than he does. A more willing but less experienced candidate, on the other hand, could be eaten alive. No one is more conscious of this than Jobs. He almost singlehandedly put together Apple’s new board; now he’s leading its efforts to find a chief executive. According to insiders, Jobs considered Apple’s offer to become chairman until late last week. ““Steve decided that it was in Apple’s best interest to leave the chairman’s position vacant,’’ says chief financial officer Fred Anderson, explaining that a topflight candidate would probably insist on being named both chairman and chief executive.

That said, Jobs may yet end up heading Apple, despite avowals that for personal and professional reasons (such as his commitment to the Pixar animation studio) his ““hat is not in the ring’’ (interview). Key board members think he would be perfect for the job, among them Campbell, Ellison and York. Yes, they’ll go for an outsider if they find the right person. But they need to move fast. Jobs is already running the company. The longer the search for a successor to Gil Amelio goes on, the more decisions he will have put into place, and the greater his stake will be in the outcome. ““My prediction,’’ says Champion, ““is that Jobs will ultimately be named chairman, and Apple’s board will be running the business.’’ The question is whether that would be the Dream Team of loyalists’ imagination - or a nightmare.