FORTUNE — Despite rapid growth in developing economies over the past decade, advanced economies continue to dominate lists of the world’s largest corporations, providing 75% of the companies on this year’s Fortune Global 500 list, and fully 91% if one excludes state-owned firms. Now emerging economy growth is slowing, suggesting that companies from these economies will remain also-rans on the list. But don’t count out these companies just yet. The possibility of a big shake-up in the corporate pecking order is worth taking seriously for a number of reasons:

The global economy is shifting: Despite recently cutting emerging market growth rates, the IMF still forecasts that these countries will account for the bulk of global growth from 2012-2018. The center of economic gravity for many sectors has already made a big shift to emerging markets. In 2000 the auto industry manufactured and sold 85% of its products in advanced economies, but that split is now half-and-half between advanced and emerging economies, with China the largest single vehicle market in the world and by far the biggest source of global growth. Even sectors such as pharmaceuticals that still do most of their business in advanced markets are starting to realize that if they let others dominate sales and distribution in emerging markets, they’ll probably never be able to win the share back.

The incumbents are slow to respond: Another reason that advanced-country multinationals’ share of the Global 500 list might shrink is that they have been slow to respond to this shift in global growth. According to McKinsey, 100 of the world’s largest companies headquartered in advanced economies derived just 17% of their total revenue in 2010 from emerging markets — though those markets accounted for 36% of global GDP and are likely to contribute more than 70% of global GDP growth through 2025. Emerging market companies are also growing faster than those from advanced nations. From 1999 to 2008 they not only grew more rapidly in developed markets — 22% vs. 12% annually — than companies from rich economies but outpaced them by even more in emerging markets: 31% vs. 13%.

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Lack of globalization at the top. When it comes to the makeup of their top management, large companies are even less global than they are with their sales priorities. Of the 375 companies from advanced economies in the Fortune Global 500, only 4% have CEOs from emerging economies. And a recent McKinsey survey of leading Western companies found that just 2% of their top 200 employees hailed from key Asian emerging markets. This is a major problem because perspectives are largely conditioned by where one is from. Hiring top talent in emerging markets has become difficult because of fierce competition from local firms. Although this talent gap could in principle be addressed by moving executives to emerging markets, according to a BCG survey of large multinationals, only 9% of the companies’ top 20 leaders are located in these markets, vs. an average of 28% of their revenues.

Long-distance trade can be costly: Doing business in emerging markets isn’t easy for advanced nation multinationals. Developing nations are much less likely to have free-trade agreements with advanced economies than the latter are with each other, and rank significantly worse on rule of law, political stability and corruption. Culturally, emerging economies are generally more hierarchical. Even geography drives a wedge: On average, emerging markets tend to be more than one-third farther away from advanced markets than the latter are from each other. These greater distances dampen all kinds of international interactions:  trade, FDI, or information flows. Consider from a U.S. perspective how much farther it is to export to China than Canada.

Corporations in the developing world are getting smarter: It is generally assumed that advanced country multinationals are capable of doing anything that their smaller, technologically backward, less marketing-savvy counterparts from emerging countries can. However, the latter possess some special capabilities of their own. A number of Chinese and Indian companies, for example, have developed low-cost capabilities that are the envy of competitors from advanced countries. Companies from emerging economies are particularly likely to have a home-court advantage. Moreover, the greater similarity between emerging economies suggests that these advantages may extend to other emerging markets as well. And as they move into each other’s markets, advanced country multinationals can’t even take their dominance at home for granted: As one management sage asks, is it easier for a poor man to learn to live like a rich man, or for a rich man to learn how to live like a poor man?

Of course, none of this is meant to suggest that the game is over for advanced country multinationals. They still enjoy significant advantages in terms of marketing, R&D, and management systems. As the entrenched incumbents, they also have a disproportionate ability to dictate the terms of engagement. But that said, emerging market multinationals have their sights firmly set on shaking things up. Advanced country multinationals need to take that possibility seriously to try to avoid ending up on the casualty list.

Pankaj Ghemawat is the Rubiralta Professor of Global Strategy at IESE and the author of World 3.0.