NEW YORK (CNNMoney.com) -- The National Highway Traffic Safety Administration has collected more than 80 complaints about steering problems in 2009 and 2010 Toyota Corollas.

The agency is not opening a formal investigation at this time, however.

The Corolla is Toyota's second most popular model.

"We are reviewing steering complaints with the Corolla to determine if a safety defect investigation is warranted, as is standard procedure with all complaints." NHTSA spokeswoman Olivia Alair said in an email.

NHTSA receives about 30,000 vehicle complaints each year, she said, and it reviews all of them.

Many of the Corolla steering complaints involve the car drifting, or being difficult to keep in line, at high speeds. Other owners complain of other, seemingly unrelated, issues such as a steering wheel vibrations or exaggerated motions from small steering inputs.

A spokesperson for Toyota was not immediately available for comment on the issue.