Severe thunderstorms were possible from the Texas-Mexico border up to North Dakota, The Weather Channel reported. Parts of Oklahoma, Kansas, Colorado, Nebraska, and South Dakota were also in the firing line.
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"Large hail and damaging wind gusts are the biggest concerns," The Weather Channel reported, adding that isolated tornadoes "can't be ruled out."
Moisture from the Gulf of Mexico meant there was a risk of more heavy rain and flash flooding across many of the same areas.
The National Weather Service issued flood warnings in several of these states, as well as severe thunderstorms and flash flood warnings for parts of Texas.
At Dallas-Fort Worth International Airport, 34 flights were canceled and 104 were delayed on Sunday, according to the tracking website FlightAware. There had been six cancellations as of 4:30 a.m. ET Monday.