For generations, American universities have been a magnet for some of the brightest scientific minds from around the world, and many of those students are setting their sights on getting more than just a diploma here.

Given opportunities for work found nowhere else, most finishing advanced degrees in science, technology, engineering and math -- four areas called STEM -- prefer to settle here. Those graduates contribute to innovation within industry that helps drive U.S. markets.

But in the global economy, engineers and information specialists from emerging nations increasingly are in demand right in their own homelands, from Mumbai in India to Beijing in China.

There are signs that some from those nations, sensing this shift in career opportunity, are becoming more inclined to return to their roots to pursue their life's work. It is escalating worries among some that the United States won't have enough talent -- homegrown or imported from overseas -- to keep pace with the demand for skilled workers in an increasingly technological society.

Already, they say, too few students from the United States choose those technical fields.

At Carnegie Mellon University, where about half of the enrollment in STEM disciplines comes from outside the United States, homeward migration has become particularly noticeable the past decade among students from countries such as India and China, said Indira Nair, vice provost for education.

There are more jobs available in those countries than before, including those with U.S. multi-national corporations that are doing more work overseas. Rising pay (though still below U.S. wages) and incentives, including some offered by governments, have tipped the scale for some who previously would have decided to forgo life in their own culture for a shot at a more lucrative career in America.

"Now they can work for Microsoft in India, and the thing of it is, now you're close to your family, so your children will get to know their grandparents," she said.

Dr. Nair, who came to the United States from India as a doctoral student in the 1960s, empathizes with such yearnings. But as a teacher and administrator, she laments the loss of students who pay their tuition but leave this country with something far more valuable -- their minds.

"You can't put a price on that," she said. "All the knowledge you gave them, they take it back home and give it to their economy rather than ours."

In some respects, the scattering of jobs and technical know-how around the globe has altered traditional notions about brain drain, experts say. Given the volume and speed of information now available, a software breakthrough occurring in Asia rather than the Silicon Valley can still offer timely benefit to a firm in the U.S. In fact, a company with an overseas presence might have even been involved in the discovery.

When employers search their ranks for the best minds to tackle a problem, it is increasingly likely the teams assembled will include a mix of workers from here and abroad. In almost every facet of science, national boundaries have blurred.

"Your X-ray at the hospital could have been read by a doctor in Australia. That is being outsourced by hospitals," said Melvyn D. Schiavelli, president of the Harrisburg University of Science and Technology. "We have to get over the notion that everything that gets done in America is going to be done by Americans in America."

What really matters is how those firms can best position themselves to take advantage of this flood of innovation occurring globally.

Even so, Dr. Schiavelli argues, there is cause for concern that college students in places such as China and India are studying science and engineering at a rate three times that of U.S. students.

He cited U.S. Labor Department research showing that 86 percent of jobs in high-growth industries will require college level work in engineering, science and technology. If America can't prepare enough of its own citizens for the work, the jobs will be filled by others.

"In the global economy, you can be marginalized if you don't ante up," he said.

Dr. Schiavelli said the world has changed radically from half a century ago when fascination with the U.S.-Soviet space race "and a couple of good teachers" started him on a path toward a scientific career. "What wasn't the case then was the dependence of every sector of the economy on the use of technology," he said.

Nowadays, it's pervasive, from the environmental design of buildings and robotic equipment in factories to the software that runs hotel reservation networks.

"Remember when you and your dad would fix the car? You'd look down into the hood and you could see the road," he said.

Today, a look into the engine reveals computer cards and sensors.

According to the National Science Foundation, there are 21.6 million scientists and engineers in the United States. Of that total, about 3.4 million are immigrants, and they are more likely than their U.S.-born counterparts to go beyond a bachelor's degree.

Thirty percent of immigrants reported a master's degree as their highest academic credential, versus 27 percent among American-born scientists, according to the data. The gap widens among doctoral degree holders. Nine percent of immigrant scientists have them, compared with 4 percent of scientists born in this country.

Among those who finish doctoral degrees in this country, 77 percent indicate a preference to remain in the United States, according to federally supported surveys.

What the government calls the "stay" rate among foreigners is even higher in STEM fields. For instance, it's 90 percent in chemistry, 88 percent in biological sciences and 87 percent in electrical engineering, according to 2006 multi-agency survey data coordinated by the National Science Foundation.

But even for the most eager to stay, navigating foreign worker rules imposed by the government can be daunting enough to send some packing. There simply aren't enough H1B visas to accommodate the number of highly skilled technical workers needed, said Emily DeRocco, president of the Manufacturing Institute and senior vice president of the National Association of Manufacturers.

She said the tone should be far different.

"I think a citizenship application and green card should be stapled to their diploma so they have a motivation to stay," said Ms. DeRocco, a former U.S. assistant secretary of labor.

To understand the problem, she said, look no further than manufacturing. She said many baby boomers still view plants as dirty, dangerous places where they would not want their children to work. But in fact, she said, they are driven by robots and other technology and are the source of 70 percent of the private research and development that is occurring in the nation.

Even with off-shoring, there are still better than 18 million jobs anchored in manufacturing in this country, Ms. DeRocco said. In surveys, 80 percent of manufacturers say they cannot find the workers with the necessary technical skills.

Foreign workers are a short-term fix, she said. A longer term solution is making sure schools are encouraging enough students to enter STEM.

"We have two choices. We can either learn to expect less and no longer be the leading economic power in the world, or we can get about the business very quickly of efficiently articulating and implementing a national innovation agenda, including education reform," Ms. DeRocco said.