The National Hurricane Center says Alex has weakened from a hurricane to a tropical storm as it moves over northeastern Mexico.
The hurricane center in Miami reported early Thursday that the storm had sustained winds of 70 mph (110 kph). It says Alex is expected to weaken as it moves further inland.
It said the government of Mexico has replaced a hurricane warning with a tropical storm warning for the coast from Rio San Fernando to La Cruz. Mexico also discontinued a tropical storm warning on the coast from south of La Cruz to Cabo Rojo and north of Rio San Fernando to the moth of the Rio Grande.
Alex made landfall late Wednesday at Soto La Marina, Mexico.
South Texas avoided the worst of the storm.
The National Weather Service in Brownsville said flash flooding and coastal flooding were a concern through Thursday afternoon.
No injuries were reported in Texas as the system drenched the Rio Grande Valley but spared the state from damage that often accompanies hurricanes.
The Queen Isabella Memorial Causeway, linking South Padre Island to the rest of Texas, remained closed Thursday.