By DAVID BARBOZA
and BRAD STONE

SHANGHAI

IF GOOGLE PULLS out of China because of frustration with government restrictions, it will not be the first time an American Internet giant has retreated from the country.

EBay and Yahoo arrived with high hopes for a market that failed to live up to their expectations. Social sites like Facebook, MySpace and Twitter have never managed to gain a significant foothold in China .

No major American Internet company has dominated its field in China, which by some measures is the world’s largest Internet market. Many experts thought Google would be the first.

“There’s no U.S. Internet company close to being a leader here,” says Gary Rieschel, founder and managing director of Qiming Venture Partners, a venture capital firm. “And most of the wounds are self-inflicted.”

While each failure has been different, analysts say the cases may help explain why Google is frustrated - not just by government censors but by its inability to catch its big Chinese rival, Baidu.

Google, an Internet Goliath with $22 billion in revenue and some of the smartest people on the planet, is getting clobbered in China, holding 33 percent of the search engine market to Baidu’s 63 percent. Google has gained significant market share since it formally entered China five years ago, but almost all of that has come from smaller rivals. Baidu also gained market share in that time.

No one expected it to be this way. America’s technology giants came here armed with cash, intellectual property and an ability to manage complex networks and introverted workers.

Google set up its China business in 2006, after it invested in Baidu and then reportedly tried and failed to buy it . Baidu, founded in 2000 when the Chinese Internet was beginning to bud, carved out a presence by offering something that Google, at first, would not: links to download pirated songs, TV shows and movies from Chinese Web sites.

Baidu claimed this was legal because the media files were not on its own computers. Google itself finally introduced a free online music service in China in 2009, with the permission of the music labels, but it has never managed to make up the lost ground.

“Searching for music is what people did early on in China,” said Felix Oberholzer- Gee, a professor at Harvard Business School who has studied the Chinese Internet market. “It was huge, and Google didn’t have it.”

Google has said that its threat to leave China has nothing to do with financial considerations.

Perhaps no company tripped up as badly in China as Yahoo. It bought a local Internet company in 2004 to expand its Web presence and compete with Baidu and the local portal Sina.com. After it failed to gain ground, Yahoo abruptly reversed course, paying a billion dollars for a 40 percent share in Alibaba, a local Internet giant, which then took over its Chinese business.

In 2004, the nonprofit group Doctors Without Borders reported that Chinese dissidents had been jailed because Yahoo released the contents of their e-mail accounts to the Chinese government. In subsequent years, Yahoo executives, including Jerry Yang, a co-founder, were brought before the United States Congress and berated over the incident.

In 2003, eBay bought EachNet, the leading Chinese auction house, and briefly controlled 80 percent of the Chinese e-commerce market. Then it was completely outmaneuvered. EBay charged for listings, while a local upstart, Alibaba’s consumer-oriented auction site Taobao.com, did not. EBay also did not offer ways for buyers and sellers to chat online, fearing they would close their transactions off the site to avoid paying fees. Taobao executives offered an instant-message service to allow customers to haggle over deals.

EBay surrendered and left China in 2006, leaving the market to Taobao, which also now dwarfs Amazon’s Chinese e-commerce site.

The most recent underachiever in China was MySpace, owned by the News Corporation, which set up a locally owned Chinese business in mid-2007. But millions of people already use the social services of local Internet companies, like Tencent, which operates an online entertainment bazaar and has a stock market value of $37 billion .

Many high-tech executives and American experts on China complain that it is not an even playing field. American companies must operate in China through locally owned firms, creating a cumbersome structure that limits their flexibility. They are also handicapped by government censorship and favoritism of local firms.

The Chinese Web over all is both vibrant and chaotic. There are thriving local blogs, entertainment and online gaming sites . Meanwhile, Chinese Internet tycoons like Jack Ma of Alibaba, Robin Li of Baidu and Pony Ma of Tencent are national figures, celebrated for their instincts and intelligence .

“The problem here is when you get down in the weeds and talk about flexibility and tactics, Chinese entrepreneurs are hard to beat,” says Mr. Rieschel at Qiming Ventures.