DALLAS - Southwest Airlines says it has grounded 128 planes after failing to inspect backup hydraulic systems used to control the rudder if the main system fails.

Southwest spokesperson Brandy King said the airline canceled about 80 flights Tuesday and expected to cancel up to 19 more on Wednesday while some inspections are done. She said the airline expected to finish "a good portion" of the inspections by Wednesday morning. The grounding covers about one-fifth its fleet.

The move surprised passengers who reported that their flights were unexpectedly delayed at airports like Baltimore/Washington International, reports CBS News correspondent Jeff Pegues.

King said that, after discovering the missed inspections, the airline immediately notified federal safety regulators and began checking the planes.

Late Tuesday night, the Federal Aviation Administration agreed to let the airline resume flying the planes while inspections are done, likely during overnight hours. FAA spokesman Lynn Lunsford confirmed that the agency approved the plan after talking with Southwest and Boeing, the manufacturer of the planes.

The missed inspections were first reported by The Wall Street Journal.

The newspaper cited the airline as saying the groundings "weren't the result of an airworthiness directive from the FAA."

King called the missed inspections inadvertent. She said the airline discovered that 128 of its Boeing 737-700 jets already had flown beyond the point at which the backup hydraulic systems were supposed to be inspected. She said safety was the airline's top priority, and it was working to fix the matter quickly.

Dallas-based Southwest is the nation's fourth-biggest airline. It has 665 jets, all of which are some version of the Boeing 737, including nearly 450 of the 737-700. That model seats 137 or 143 passengers, depending on the layout.

The Associated Press contributed to this report.