DALLAS >> Federal officials have agreed to let Southwest Airlines Co. keep flying planes that missed an inspection of a backup rudder system if the planes are checked in the next five days.

Southwest grounded 128 planes — about one-fifth of its fleet — on Tuesday after discovering the missed inspections.

Southwest spokeswoman 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 missed inspections involved hydraulic systems used to control the rudder if the main system fails. King said that after discovering the lapse, Southwest immediately notified federal safety regulators, took the planes out of service and began checking them.

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.

Dallas-based Southwest is the nation’s fourth-biggest airline. It has 665 jets, all of which are some version of the Boeing 737. Tuesday’s groundings involved nearly one-third of its 737-700 models, which seat 137 or 143 passengers, depending on the layout.

Southwest was fined in 2009 for failing to inspect dozens of planes for cracks in the fuselage. Southwest agreed to pay $7.5 million to settle with the FAA, which had sought a $10.2 million penalty.

In 2011, the FAA ordered extensive inspections of some of Southwest’s older 737s after a 5-foot hole burst open in one plane in mid-flight, forcing an emergency landing at a military base in Arizona.