Construction companies added to their payrolls in 39 states between September 2013 and September 2014, according to figures analyzed by the Associated General Contractors of America.

Job growth was especially strong in California, Texas, Illinois and Louisiana, the association said, citing Labor Department data.

“Construction firms in most states have been expanding during the past year,” said Ken Simonson, the association’s chief economist. “But as those firms expand, they have to work harder to attract their skilled craft workers and key construction professionals.”

The fact some companies cannot find workers may be surprising, said Stephen E. Sandherr, the association's chief executive officer, but it’s a fact.

"Hard as it is to imagine, given what this industry has been through the past few years, but many firms are very worried about their ability to find, recruit and retain qualified workers as the industry continues to rebound," he said.