At the same time, though, a source familiar with the situation says DuPont has seen a lot of support for its side.

On Monday, the influential proxy advisory service, Institutional Shareholder Services, said shareholders of DuPont (DD) should elect corporate raider turned activist hedge fund manager Peltz and John Myers, who is a former GE executive and is also a Peltz nominee, to the chemical giant’s board of directors. DuPont has fought adding any of Peltz’s proposed nominees, especially Peltz.

In the report ISS wrote, “It seems eminently clear that there is a compelling need for a minority change at the board level.”

Peltz’s hedge fund Trian owns $1.8 billion worth of DuPont’s shares, or 2.7% of the company. He initially proposed breaking up the chemical company, but has since said he is open to any solution that brings down costs, one of his main beefs with DuPont’s current management. DuPont has said that Peltz’s break-up plan would be bad for long-term shareholders, painting Peltz as someone who is only interested in a short-term stock boost.

The DuPont proxy fight, which Peltz launched in January, has been one of the most closely watched match ups between an activist investor and a corporation recently. Activists have won small skirmishes with big companies. Carl Icahn got Apple to increase its dividend. Valueact, another activist hedge fund, was granted a board seat at Microsoft. But if Peltz were to win, DuPont would be the first fight where an activist was able to force their way onto the board of a major Fortune 500 company, and a company that prior to Peltz’s campaign few thought was struggling. DuPont’s shares have risen 40% in the past two years.

In a statement, Peltz said, “We are deeply gratified that ISS supports our efforts to hold the Board accountable for DuPont’s consistent underperformance.” Another vote of confidence for Peltz: DuPont’s shares rose $3 to just over $74 on the ISS news.

Nonetheless, the ISS’s report wasn’t a total win for Trian. The hedge fund is seeking four seats on DuPont’s board. ISS said shareholders should give Peltz two. The report also said that ISS didn’t think DuPont was a broken company. And ISS said it disagreed with Trian’s claim that DuPont has bad corporate governance.

Other parts of the report were odd. At one point ISS said that the question “easiest to answer” that has been raised in DuPont’s proxy fight was whether the company should be broken up. The answer: ISS said it had no clue. Not so easy after all.

Other parts of the report seemed to borrow heavily from Peltz’s analysis. ISS sided with Peltz’s analysis that DuPont’s profit margins and bottom line have been disappointments. And, like Peltz, it cited Axalta, the paint business which DuPont spun-off and has done well since, as a sign that DuPont’s costs are high. DuPont has said that 2011 isn’t a fair starting point. The company says if you start from when its current CEO Ellen Kullman started in 2009 and only include the company’s core businesses, not ones DuPont has sold off, closed or is in the process of spinning out, the company’s earnings are up 19% a year. Company officials agree Axalta has performed well after leaving DuPont, but they say that is more a factor of the economy and not the company’s mismanagement.

ISS’s decision and report may not have been that much of a surprise to close watchers of these battles. ISS often sides with activist investors. And since DuPont has so many individual shareholders, who tend to vote with management and are often not aware of proxy advisory services, ISS’s decision and the decision of other proxy advisory services like Glass Lewis, which is scheduled to be out later this week, may not matter as much in this case. There have been number of cases in which ISS sided activists, and shareholders have still voted with the company.

People familiar with DuPont’s effort to get shareholders to vote for the company’s directors and not Trian’s says the company has a lot of support and that momentum has been building for its side. In the past, Trian officials have also said they are optimistic about winning the shareholder vote.

In a statement, DuPont said, “We are confident that shareholders will do their own analysis and believe they recognize that DuPont has the right strategy and right Board to continue overseeing the successful transformation of DuPont.”

DuPont shareholders are scheduled to vote on May 13.