About 60 percent of job specs processed by the recruitment firm Hudson in Singapore, for example, now require Mandarin, said Andrew Tomich, the company’s executive general manager in Singapore. Five years ago, he said, the percentage was half that.

“Even in the last 12 months, there’s been a steady increase in Singapore for Mandarin-speaking candidates,” he said. “We can feel it with every breath we take.”

In Hong Kong, which is a stepping stone to mainland China, the percentage of jobs requiring Mandarin or Cantonese has climbed to more than 80 percent, according to Aruna Alimchandani, director of the commerce and industrial unit at Hudson in Hong Kong. That is up from about 70 percent just a few years ago.

In mainland China in the 12 months through October 2012, expatriates ended up in just 5 percent of the jobs filled by Hays, a recruitment agency that specializes in white-collar jobs. One year earlier, the number was 11 percent, said Christine Wright, who heads Hays’s operations in Asia.

It is not that companies do not want to add employees. A recent survey by Hudson showed that the vast majority of companies in mainland China, Hong Kong and Singapore planned to increase their numbers of employees or keep staffing levels steady this quarter. Many, in fact, have to work hard to attract and retain workers.

But, job market experts say, employers are more eager than ever to ensure that the employees they do hire match their expectations.

On the cost front, that means avoiding the extra expenses that can come with hiring foreigners — relocation costs, for example, or school fees for children. Many have also become more eager to fill positions with people who are unlikely to leave again soon.