Dora was downgraded late on Friday from a Category 1 hurricane to a tropical storm by meteorologists Mexicans.
The storm was at 00.00 GMT 310 kilometers south of the resort town of Cabo San Lucas in Baja California Sur (west).
The storm now has sustained winds of 110 kph and gusts of 130 mph, said National Weather Service in its latest report.
A Category 1 hurricane on the Saffir-Simpson scale has winds between 118 and 153 km / h. Dora had reached winds of 250 km / h on Thursday, which made it a level 5 hurricane, the maximum.
The authorities of the state of Baja California Sur decreed the alert and expect heavy rains in the coming hours.