The number of foreign students admitted to graduate schools at American colleges and universities grew in 2008 for the fourth straight year, but the rate of increase over the previous year declined for the third consecutive year, according to survey results released by the Council of Graduate Schools. Based on previous years' data, this year's 4-percent increase will mean only a small gain in first-time enrollments of foreign students for the fall, said Kenneth E. Redd, the council's director of research and policy analysis. Admissions offers to students from China, India, and South Korea, the three nations that together account for nearly half of all foreign graduate students in the United States, all reflected the slowing trend in 2008. For students from China, the rate of growth in such offers slowed from 24 percent to 16 percent, and for those from India, it fell from 17 percent to 2 percent. Offers to students from South Korea, which had declined last year by 2 percent, lagged even further this year, posting a 3-percent drop. Mr. Redd said the slowdown from those three countries can largely be attributed to their own efforts to increase graduate enrollments at home. Furthermore, this year's overall increase in foreign admissions follows growth rates of 8 percent last year and 12 percent in 2006.