The Pacific tropical storm, Hilary, is bringing massive rainfall to the western United States (U.S.) of California, including the coastal cities of San Diego and Los Angeles.
The weather service warned that Hilary would bring rainfall exceeding the average annual amounts in some places.
Desert areas would be especially dangerous due to the risk of flash floods.
California Governor, Gavin Newsom, declared a state of emergency for large parts of southern California.
The U.S. Weather Service had warned of catastrophic and life-threatening flooding likely over northern Baja California and portions of the South-Western U.S. through Monday.
The storm had weakened over the course of Sunday and had been downgraded from a hurricane to a tropical storm.
In the south-west of the U.S., Hilary had already brought heavy rain over the weekend.
According to the National Hurricane Centre, the storm crossed the border into southern California late on Sunday afternoon after bringing strong winds and heavy rain to the Mexican Baja California Peninsula.
The storm battered the Baja coast with large waves and the Mexican weather service reported sustained wind speeds of 110 kilometres per hour.
According to media reports, Hilary has already claimed two lives.
One man died as a result of flooding along the Pacific coast of north-west Mexico, as the newspaper El Universal reported.
The report said that a van was washed away in the state of Sinaloa, while the driver was found dead a few kilometres away.
In the town of Mulegé in Baja California, another person was killed while trying to cross a river, according to the newspaper Milenio.
