DOZENS of new students crowded into a lobby of the University of Delaware’s student center at the start of the school year. Many were stylishly attired in distressed jeans and bright-colored sneakers; half tapped away silently on smartphones while the rest engaged in boisterous conversations. Eavesdropping on those conversations, however, would have been difficult for an observer not fluent in Mandarin. That’s because, with the exception of one lost-looking soul from Colombia, all the students were from China.

Among them was Yisu Fan, whose flight from Shanghai had arrived six hours earlier. Too excited to sleep, he had stayed up all night waiting for orientation at the English Language Institute to begin. Like nearly all the Chinese students at Delaware, Mr. Fan was conditionally admitted — that is, he can begin taking university classes once he successfully completes an English program. He plans to major in finance and, after graduation, to return home and work for his father’s construction company. He was wearing hip, dark-framed glasses and a dog tag around his neck with a Chinese dragon on it. He chose to attend college more than 7,000 miles from home, Mr. Fan said, because “the Americans, their education is very good.”

That opinion is widely shared in China, which is part of the reason the number of Chinese undergraduates in the United States has tripled in just three years, to 40,000, making them the largest group of foreign students at American colleges. While other countries, like South Korea and India, have for many years sent high numbers of undergraduates to the United States, it’s the sudden and startling uptick in applicants from China that has caused a stir at universities — many of them big, public institutions with special English-language programs — that are particularly welcoming toward international students. Universities like Delaware, where the number of Chinese students has leapt to 517 this year, from 8 in 2007.

The students are mostly from China’s rapidly expanding middle class and can afford to pay full tuition, a godsend for universities that have faced sharp budget cuts in recent years. But what seems at first glance a boon for colleges and students alike is, on closer inspection, a tricky fit for both.

Colleges, eager to bolster their diversity and expand their international appeal, have rushed to recruit in China, where fierce competition for seats at Chinese universities and an aggressive admissions-agent industry feed a frenzy to land spots on American campuses. College officials and consultants say they are seeing widespread fabrication on applications, whether that means a personal essay written by an agent or an English proficiency score that doesn’t jibe with a student’s speaking ability. American colleges, new to the Chinese market, struggle to distinguish between good applicants and those who are too good to be true.

Once in the classroom, students with limited English labor to keep up with discussions. And though they’re excelling, struggling and failing at the same rate as their American counterparts, some professors say they have had to alter how they teach.

Colleges have been slow to adjust to the challenges they’ve encountered, but are beginning to try new strategies, both to better acclimate students and to deal with the application problems. The onus is on them, says Jiang Xueqin, deputy principal of Peking University High School, one of Beijing’s top schools, and director of its international division. “Are American universities unhappy? Because Chinese students and parents aren’t.”