FORTUNE — Kent Kedl knew he had big problems last year when he took the helm of the Asia practice of London-based management consulting firm Control Risks. In his first six months, Kedl sat in his Shanghai office and listened to the same story at least four times from top managers: A competitor offered to hire them away for three times their salary.

All four people left the firm, handing Kedl the daunting task of filling those jobs with qualified leaders who had knowledge of the region. “These guys are getting calls every week by headhunters, and it’s problem No. 1 on everyone’s mind here,” says Kedl.

Hiring in the U.S may still be sluggish, but when it comes to finding and keeping top management in emerging markets like China, it’s a sellers’ market akin to pre-financial crisis America. Some 42% of company leaders say filling jobs with good people abroad is one of their toughest challenges, according to a 2011 survey of 992 C-level executives by Ernst & Young. In India, for instance, 67% of employers say they struggled to build effective management teams in that country, up from 16% in 2010, according to a different survey by global staffing organization ManPower.

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While India has benefited from impressive GDP growth and watched its IT sector blossom into a $100 billion industry in the past two decades, its focus on developing engineering talent has left the country dry of Indians with leadership and management skills, says Srini Kandula, vice president of human resources for iGATE, a Freemont, Calif.-based outsourced software developer with 28,000 employees and operations in Bangalore.

“Everyone prefers leaders who are exposed to global business practices, and supply is limited,” says Kandula, so companies across a broad array of industries compete for the same people.

In Russia, Edward Mermelstein spent six months training and relocating top-level executives to run the Moscow office for Rheem Bell & Mermelstein, a corporate law firm based in New York. But in the past two years, local competitors poached two of his executives, offering them nearly double their salaries. Mermelstein says the same scenario is playing out with many of the firms’ other big banking clients there.

“The competition is cutthroat, and they don’t give you two-week notices. If they leave, they just leave,” says Mermelstein, the firm’s principal.

Confronted with these labor shortages, the typical response has been to parachute in expatriate executives, but that strategy is not always successful. Just 29% of executives surveyed by Ernst & Young said their companies effectively relocate employees without big disruption.

Moving those expats can be even more challenging with the U.S. housing market still in a slump. It’s a costly endeavor to buy — and then sell — an employee’s home to send them abroad. And these execs are not always the ideal hire: Local management teams often have deep knowledge and understanding of national cultures, markets, and worker psychology that most companies need for long-term stability, says Mark Murphy, CEO of Leadership IQ, an Atlanta research and management consulting firm.

Beer-maker Anheuser-Busch InBev (BUD) is hedging its bets for the future by recruiting promising leaders straight out of college, including foreign nationals while they are living outside their home countries. The company recently recruited two Chinese graduates from the University of Washington who joined the beer-maker’s global management trainee program. Managers who perform well are put on a 10-year track for global C-level jobs. Three of the company’s global division presidents and two C-executives came up this way. “It’s proven to be successful,” says Bieke Teerlinck, who oversees the company’s trainee program.

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To ensure top Indian executives stay today, iGATE began to offer stock options, and the company has managed to keep its C-team in India for several years even while competitors offer executives jobs for two to three times the pay. iGATE has also placed an emphasis on identifying Indians within the company who could be groomed for top jobs, says Kandula.

After losing four top people in China, Control Risks’ Kedl started laying out a clear career path for new management hires, showing them the specific steps for more leadership opportunities, pay, and job descriptions. He also gives managers regular performance reviews and, when appropriate, offers them raises and promotions before they even ask. “The whole ‘people are the most important assets’ thing is not corporate bologna,” he says. “That’s the hard-core truth. You really learn that in a market like China.”