Since becoming chief executive of the Walt Disney Company two years ago, Robert A. Iger has dazzled Wall Street by delivering soaring profits and moving aggressively to fix trouble spots, the New York Times reports.

But now, for the first time under Mr. Iger’s watch, Disney is sailing into some choppy waters. Two of the company’s four growth engines , theme parks and consumer products , turn on the health of the economy, which indicators suggest is slowing. Striking television and movie writers threaten advertising income at ABC, which Disney owns.

Hollywood’s union problems also afflict Disney’s film studio, which faces life without a new installment of its money machine, “Pirates of the Caribbean,” and could be dealing with delays on big-screen franchise films like “High School Musical 3.”

How Mr. Iger navigates these and other challenges will either solidify or puncture his emerging reputation as a blockbuster chief executive, analysts say. “Bob has done a spectacular job so far, but this is a test,” said Jessica Reif Cohen, the chief media analyst at Merrill Lynch. “The easy growth is over.”

Disney’s recent success poses a conundrum. When a company delivers five consecutive years of double-digit growth in operating income, as Disney has done, anything less looks disappointing to Wall Street. Mr. Iger became chief executive in October 2005 after a period in which the Magic Kingdom was rocked by a shareholder revolt , which toppled his predecessor, Michael D. Eisner , and trouble in its core animation business.

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