Scientists, engineers and other skilled professionals seeking emigration to the US could face waits of a decade or more before receiving the coveted “green card” that allows them to remain permanently in the country.

This month the annual quota even to apply for employment-based green cards was exhausted for highly skilled professionals from China and India, and for less-skilled workers from all other countries, according to the State Department. The wait to apply for a green card has now grown to more than five years in many cases.