Across the United States, 33 million people face the risk of severe weather Sunday.
The greatest potential for severe storms will be from parts of southeast Oklahoma into northeast and east-central Texas.
The storms could spark tornadoes, particularly over northeast Texas.
Large hail could also slam parts of the region.
Flood rescues were under way in Denton County, Texas, on Sunday, just outside the Dallas-Fort Worth area. Aerial images from CNN affiliate KTVT showed severe flooding and people being lifted and then carried to safety in a helicopter.
The threat will move east Monday, including the cities of Cleveland, Houston and Memphis, Tennessee.
On Sunday, a tornado struck the small South Dakota town of Delmont.
Approximately 20 buildings were damaged, and residents were being asked to leave because of unsecured propane tanks, Department of Public Safety spokeswoman Kristi Turman said. There were no serious injuries from the storm, she said, but Delmont had no power, no water and no telephones.
A fierce storm also swept through Lake City, Iowa, ripping most of the roof off a local high school, said Mayor Gary Fahan. The people who were inside the school for an award ceremony had left the building when they heard the tornado sirens, he said, reporting that there were no injuries.
On Saturday, a tornado that struck Eastland County, Texas, west of the Dallas-Fort Worth area, killed one person and injured another critically, according to the local fire department.
Meanwhile, an intense late-season winter storm is moving over the Central Rockies and into the Plains. The mountains near Crestone, Colorado, have seen more than 17 inches of snow.
Parts of Wyoming and Nebraska are also getting hit, with heavy snow and reduced visibility making travel extremely dangerous.
Separately, Tropical Storm Ana made landfall early Sunday in South Carolina.