I usually try to control myself and resist giving compliments or unsolicited advice to people I don’t know well. But I recently did just that. I emailed letters to Lee Scott, C.E.O. of Wal-Mart, and Jeff Immelt, C.E.O. of General Electric. I wanted to share with them some of my thoughts about their businesses. Both companies are leviathans that have struggled recently to grow in ways that satisfy shareholders. Wal-Mart, I wrote to Scott, has created a phenomenal opportunity for itself by offering in-store health clinics and, in the process, may transform the U.S. health-care industry. G.E., I told Immelt, could boost its fortunes by complementing its experience in power generation with building an electric car.

In my position as a lecturer at Stanford Graduate School of Business, I’ve been working with my colleague Professor Robert Burgelman to examine how large companies can defeat the law of big numbers. Successful businesses sooner or later encounter a situation in which the reward for their success becomes a punishment of sorts. The reward is that they get big. The punishment is that when they get big, it gets harder and harder for them to grow. And then their investors pile on the abuse.

In looking at various companies that have been hindered by their own success, we found that under certain conditions a firm can create a new growth spurt for itself by entering an entirely different industry. The target industry must be stagnant and populated with companies that cling to doing business the way they always have. The corporation that enters this environment with an innovative product or service can shake up the status quo and reap big profits. Burgelman and I call this phenomenon cross-boundary disruption, or XBD for short.

The defining example of this kind of move is Apple’s incursion into the sluggish music business with the introduction of the iPod in 2001 and then the iTunes music store in 2003. At the time, Apple faced market saturation in its niche. (Its relatively high-end computers were stuck with a single-digit market share.) It had all the resources of an established, well-run corporation: highly skilled employees, brand appeal, and access to capital. And it was hungry for growth. Since Apple entered the music business, the company’s profit has increased more than 3,000 percent, from $57 million in 2003 to nearly $2 billion in 2006.

The XBD phenomenon is something separate from the more familiar pattern of startups forging industry change in steps. Clayton Christensen described that process in his book The Innovator's Dilemma. In Christensen’s scenario, a small company penetrates an industry by first establishing a position in the least demanding portion of it and then progressing into more-demanding segments. Christensen shows how minimills entered the U.S. steel industry in the 1970s by concentrating on the low-margin area of the market that the established players had largely given up on. The new companies grew until they were strong enough to attack larger and larger market segments. By 2000, these minimills had increased their production to almost 50 percent of the raw-steel market.

Cross-boundary disruption is different. I’m talking about established giants seeking to transform markets other than their own. It's Apple jumping into music. It’s Wal-Mart entering health care. Or as my email to Immelt urged, it could be G.E. building an electric car and taking on the energy industry. These are companies big and powerful enough to solve intractable, industrywide problems and produce lasting change.

When Apple launched iTunes, music labels were desperately struggling with the impact of digital technology. CD sales were declining as fans grabbed music from file-sharing sites. Between 2000 and 2006, according to the Recording Industry Association of America, CD shipments tumbled 35 percent—from 942.5 million to 614.9 million. Executives at record companies should have worried that things would get worse, yet their attitude seemed disconnected from reality. About 10 years ago, I listened in disbelief as a top music executive asserted that people like the experience of going into stores “to see and touch” CDs and prefer to get their music that way. This view remained widespread even as illegal downloading of music went mainstream.

Meanwhile, Apple was enjoying a strong position in the computer industry but found that it needed to look beyond its native market in order to create growth. The company’s tiny market share suggested that sales of its somewhat pricey products had peaked. As an established brand, Apple could afford to develop a digital distribution system and attack the entrenched players. Startups like Napster could not, and they were easily thwarted by the record companies.

Interestingly, Apple also had an advantage in C.E.O. Steve Jobs. Executives of potential XBDs are often blind to cross-boundary opportunities because they tend to focus only on their own markets—even though other industries may offer huge potential. Burgelman and I call this the disrupter’s paradox. Those who are strong enough to mount an attack on another industry will rarely be aware of the opportunity to do so. Jobs, however, had a long involvement with the media industry through his investment in Pixar Animation Studios, the creator of Toy Story and other megahits. This experience most likely helped him avoid the disrupter's paradox.

Since Apple introduced the iPod and iTunes, it has sold more than 100 million of the digital music players and more than 3 billion song downloads. Profits have soared. Meanwhile, CD sales continue to fall. In the first six months of 2007, they dropped 19 percent, according to Nielsen SoundScan.

Digital technology is bound to facilitate other cross-boundary disruptions. Google’s move into advertising with its AdSense program may prove to have a revolutionary impact on advertising, not only because it diverts revenue away from traditional media, but also because it allows for increasingly well-targeted context-sensitive ads in which the commercial message is presented to readers or audiences at precisely the right time and closely matches their interests. Whoever has a good understanding of these possibilities and can move aggressively might redefine the business of advertising and, by extension, the media that carry commercial messages. It’s not surprising that a rule breaker like Google is driving this change.

In my email to Scott, I wrote that transforming the health-care industry could become "the most appropriate emerging example" of cross-boundary disruption. I should have said most important. The health-care industry ultimately helps define each of our lives, our children’s well-being, and the way we spend our golden years. It is huge, big enough to provide fertile ground for any would-be XBD. In the U.S., this market is worth an estimated $2.26 trillion, more than six times the size of Wal-Mart, which reported revenue of $349 billion last year. The industry's structure is inscrutable. Almost anyone who has had to navigate physician networks, hospital chains, and giant insurance companies ends up wishing that somebody would do something to fix health care. What’s more, the medical system’s willingness—and ability—to change is questionable. It should be an attractive target for a player from another industry with the resources and core competencies to attack it.

Wal-Mart is in an excellent position to assume the role of the disrupter. It has an incredible record of innovation and execution, yet it has grown to the point where its very success has led to problems. Wall Street analysts characterize this giant as having saturated its market with more than 4,000 stores. Same-store sales have fallen from year to year, and Wal-Mart's share price has dropped from its all-time high of $69, in December 1999, to $45 in October.

The need to do something different must have weighed on management, and its solution may prove to be a new disruptive phenomenon. Two years ago, Wal-Mart launched a pilot program of in-store clinics. These facilities provide standard medical treatments and services, ranging from vaccines for measles to cholesterol screening, all at low fixed prices. A standard checkup, for example, tops out at $65. Since 2005, Wal-Mart has opened 78 clinics in 13 states and has plans for up to 400 more in the next three years. If these succeed, the company intends to build up to 2,000 by 2014.

Wal-Mart's entry into health care may effect profound change by offering direct-to-consumer services and driving down prices for commodity services. Scott’s company is the master of this, and the health-care industry is, by and large, not used to competition. The basic-services segment is a less-demanding, low-end portion of the market not favored by the health-care giants. This plays well to Wal-Mart's strengths.

Wal-Mart, much like Apple, displays the key attributes of an XBD. And in just the way that Apple succeeded where Napster failed, Wal-Mart's size, brand appeal, strong finances, and resources should help it overcome resistance from hospitals, drug companies, and insurance providers. Given its legendary capability to innovate and execute, Wal-Mart may emerge as a superb XBD.

Judging from the comments of the business press and analysts, G.E. has a problem similar to Wal-Mart's: It’s too big. The company's market capitalization is $414 billion, and last year's revenue was $152 billion. Profits that inch up or down don’t seem to move the stock much. Something extraordinary is required.

What could be an opportunity worthy of the awesome resources held by one of the most aggressive corporations of our time? What could make G.E. into an XBD? In my email to Immelt, I suggested that he focus the company, or part of it, on developing an electric car.

A successful disrupter of the huge and complex energy industry has to be big, patient, and daring. I think G.E. has these qualities. Carmaker incumbents like General Motors, Ford, and Chrysler, as well as energy providers like Exxon Mobil, Royal Dutch Shell, and BP, seem reluctant to adapt to the needs of our economy, the environment, and our national security. It’s hard to think of a better fit than G.E.

G.E. Energy, which reported a profit of $3 billion on revenue of $18.8 billion in 2006, would likely benefit from a shift toward electric-powered transportation. It could tackle both an electric car and the construction of the infrastructure that electric vehicles would require. The use of electricity in transportation would allow us to exploit not only oil but also wind, hydro, nuclear, and photovoltaic energy, as well as coal and gas. This is a monumental change, and it is the only way our country can shed its dependence on foreign sources of energy.

I have no idea how much G.E. should spend on such an effort or how soon the behemoth could expect it to be profitable. But I do know that the needed funds are a match for G.E.’s vast balance sheet. Tesla Motors, a Silicon Valley startup, says it spent less than $105 million to develop its line of superfast electric vehicles. It's exciting that Tesla’s Roadster accelerates faster than most Porsches, but does the tiny carmaker have the resources to take on Detroit and the oil companies? G.E. does. Plus, the company’s name already reflects such a move.

I'm still waiting for Immelt to write back. And I’m wondering if he will. Maybe he’s already doing what he needs to and doesn’t want to give away G.E.’s secret. Scott hasn’t written back either. But Wal-Mart did hire Dr. John Agwunobi, the former assistant secretary for health at the U.S. Department of Health and Human Services, as senior V.P. to oversee the company’s health-care effort. And it continues to open more in-store clinics. Perhaps that’s Scott’s answer. If so, it's more eloquent than words.