This marks the second time that Yahoo has snubbed Levinsohn, 48, who previously had been best known for overseeing the Internet operation for Rupert Murdoch's News Corp.
Levinsohn had been vying for the CEO job after Bartz's firing, only to be passed over when Yahoo lured Thompson away from eBay Inc.
"Marissa's first order of business should be convincing Levinsohn to stay," Gartner's Weiner said. "If he leaves, there will be an exodus" among the Yahoo employees working on the content for the company's website.
Mayer declined to comment on any discussions she might have planned with Levinsohn.
Weiner views Mayer's decision to join Yahoo as a "no-lose" proposition for her.
"If she can pull this off and turn around Yahoo, it will make her legacy," he said. "If it doesn't work out, she can still walk away with great class and dignity."
Mayer starts at Yahoo Tuesday, when the challenges facing her should come into sharper focus with the scheduled release of the company's second-quarter earnings. The results are expected to show Yahoo's revenue growth remains sluggish, even as advertisers are spending more to promote their products and services on the Internet. Most of that money, though, has been flowing toward Google and Facebook.
Mayer said she intends to skip Yahoo's conference call to review the second-quarter numbers so she can spend more time meeting with the company's senior management team.
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