NEW YORK (CNN/Money) - Don't expect Cola-Cola shareholders to "relax with a Coke" when they gather for their annual meeting Wednesday.

In fact, some analysts predict the meeting in Wilmington, Del., between Coke's management -- still in search of a new chief executive -- and some disgruntled high-profile investors lobbying for the removal of board members could make for a contentious event.

"The turmoil in the boardroom and the goings-on with the CEO succession should dominate the agenda," said Debbie Wang, analyst with Morningstar.

And while the world's largest beverage maker struggles to get its corporate house in order, rival PepsiCo has fractionally boosted its share of the U.S. soft drink market while Coke's share has edged lower.

Coke (KO: Research, Estimates) is also expected to report its first-quarter results Wednesday morning. Analysts surveyed by First Call forecast a profit of 43 cents a share, up from 37 cents a share a year earlier.

Whatever the numbers the company reports, industry watchers say Wall Street seeks answers abouts three issues -- leadership, boardroom intrigue and eroding market share.

Coke began its search for a new chief in February after announcing Douglas Daft, current chairman and CEO, would retire at the end of 2004.

The obvious assumption, at least among analysts, was that president and chief operating officer Steve Heyer, the No. 2 man at Coke, would make a smooth transition into the top job. But the scenario took a different turn when Coke instead hired an executive search firm to find a suitable candidate for the slot.

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Morgan Stanley analyst Bill Pecoriello wrote in a research report Monday that Gillette CEO Jim Kilts has emerged as the frontrunner for the post.

"We believe Coke's board is potentially within two weeks of announcing the new chairman/CEO. Industry sources lead us to believe Jim Kilts is the leading candidate," Pecoriello said. "Kilt has one of the best track records in the entire consumer products sector, having led Gillette, Nabisco and Kraft. We believe his appointment will be viewed favorably by investors."

And as Wang pointed out, another point in Kilt's favor is his strong ties with billionaire investor Warren Buffett, who is a large shareholder of both Coke and Gillette (G: Research, Estimates).

The California Public Employees' Retirement System (Calpers), the nation's largest pension fund and a prominent shareholder with about 12.7 million shares of Coke, has said it will vote against the re-election of nine of Coke's board members, including Buffett, citing the directors' conflicting business interests with Coke.

Additionally, the proxy advisory firm Institutional Shareholder Services (ISS), which is asking Coke to split the job of chairman and CEO, said it would urge shareholders to withhold votes for Buffett. It cites concerns about Buffett's independence, given that some subsidiaries his Berkshire Hathaway have had business dealings with Coke.

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Buffett owns 8.2 percent of Coke's shares.

Even though Coca-Cola is still the U.S. market leader, the company's share of the $63 billion U.S. soft-drink market fell by 0.3 percent to 44 percent in 2003, according to Beverage Digest. Both Coke Classic and Coke's lemon-lime soft-drink Sprite lost ground last year, while Vanilla Coke was among the worst performing brands, along with Diet Coke with Lemon.

Purchase, N.Y.- based PepsiCo's, the No. 2 soft-drink maker, grew its U.S. market share 0.4 percent to 31.8 percent. PepsiCo had a number of successes last year. Sierra Mist became a top-10 brand and Diet Pepsi posted the strongest growth of any cola in the top-10 cola category.

Coke expects to launch the "C2" mid-calorie cola on June 16.

Industry observers say innovation of beverage products is really a key driver of sales for both companies. Coke said Monday it would debut "C2" -- a new low-carb cola -- this summer ahead of Pepsi's summer launch of its new "Pepsi Edge" low-carb version.

The soft drink market, however, is experiencing sluggish sales for the fourth consecutive year. "There's a noticeable shift away from carbonated drink consumption and toward bottled water and health drinks," said Morningstar's Wang.

According to market research firm Beverage Marketing Corp., bottled water now ranks as the second largest beverage category in the United States on a volume basis, surpassing beer, coffee and milk.

"The real concern is what is Coke doing to address this trend and take advantage of it. Pepsi has done much better than Coke both in the bottled water and health drinks categories," Wang said.  

-- analysts quoted in the story do not personally own shares of the Coca-Cola and their firms do not have an investment banking relationship with the company.