The week got off to a rough start for airline passengers in cities like Dallas, Fort Lauderdale and Orlando with American Airlines and Spirit Airlines canceling hundreds of flights on Monday.

According to flight-tracking website FlightAware.com , American has canceled more than 450 flights and experienced nearly 700 delays nationwide as of 5 p.m. ET Monday. Meanwhile, Spirit has canceled 279 flights, or 36 percent of its schedule. The low-cost carrier also reported nearly 170 delays.

Severe thunderstorms wreaked havoc on American's Dallas/Fort Worth International Airport hub over the weekend, with the airline forced to cancel 283 flights on Sunday. In addition to weather, American attributed the issues at DFW to air traffic constraints. According to an internal list reviewed by CNBC , at least 30 of the cancellations were due to a lack of crew.

Spirit pinned its disruptions on "a series of operational challenges."

"We’re working around the clock to get back on track in the wake of some travel disruptions over the weekend due to a series of operational challenges," the airline said in a statement. "We understand how frustrating it is for our guests when plans change unexpectedly, and we’re working to find solutions. We ask guests to actively monitor their emails and flight status before heading to the airport."

The widespread cancellations led to crowded ticket counters at Florida's Fort Lauderdale-Hollywood International Airport and Orlando International Airport, where passengers waited in long lines to speak to employees about rebooking options.

Other carriers also experienced significant delays on Monday, with Southwest forced to delay nearly one-quarter of its schedule and Allegiant experiencing delays on nearly three out of 10 flights, according to FlightAware.com.

As always, air travelers are advised to check their flight status with their airline prior to arriving at the airport.