SEOUL — Each fall, thousands of students from South Korea arrive on American campuses. They come from a culture that views education as the key to success, where mothers and fathers save to send their children overseas. On top of tuition, parents shell out for test prep and cram schools, supplemental English lessons and recruitment agents to shepherd them through an unfamiliar admissions process. In the past, only a small elite pursued advanced degrees internationally; today, many sons and daughters of the nation’s emergent middle class go abroad.

This is South Korea but the description could fit China equally well.

Recently however, after years of robust enrollment increases, graduate applications from South Korea to American colleges have fallen off; and last year the number of South Korean undergraduates in the United States also dropped. Fewer South Koreans study in the United States now than did five years ago.

South Korean students who study abroad often find that they lack the local connections to get a job when they return home, says Jaeha Choi, director of student recruitment and admissions at SUNY-Korea, the State University of New York’s campus outside Seoul, South Korea’s capital.

Softening interest from South Korea, the third-largest supplier source of international students to the United States, could serve as a warning to American institutions that have grown to rely on tuition revenue from China, the largest source.