SAN FRANCISCO — Yahoo still has credibility issues, even after casting aside CEO Scott Thompson because his official biography included a college degree that he never received.

The troubled Internet company’s next challenge will be convincing its restless shareholders and demoralized employees that the turnaround work started during Thompson’s tumultuous four-month stint as CEO won’t be wasted.

It won’t be an easy task, given that Yahoo Inc. has now gone through four full-time CEOs in a five-year stretch marked by broken promises of better times ahead. Instead, Yahoo’s revenue and stock price have sagged during a time when rivals such as Google Inc. and Facebook Inc. are growing as advertisers spend more money online.

“It looks like there is going to be at least several more months of indirection” at Yahoo, said Adam Hanft, who runs a brand reputation consulting firm.

Yahoo’s hopes are now resting on Ross Levinsohn as its interim CEO. Levinsohn had a successful stint running Internet services within Rupert Murdoch’s media empire at News Corp. before one of Yahoo’s former CEOs, Carol Bartz, hired him in November 2010 to help her in her mostly fruitless attempt to fix the company.

Thompson, who was hired as Yahoo’s CEO in January to fill a void created by Bartz’s firing, had promoted Levinsohn last month to oversee the company’s media and advertising services throughout the world.

“The situation at Yahoo is a mess,” Macquarie Securities analyst Ben Schachter wrote in a Monday research note. “It remains unclear how the new management will turn things around at Yahoo.com.”