Tropical Storm Elida swirled off Mexico's Pacific coast Tuesday while Douglas pulled away -- but the double hit was dumping heavy rains in much of Mexico, the national weather service reported.

"Tropical Storm Elida remained stationary 135 kilometers (85 miles) southwest of Punta San Telmo, Michoacan," the weather service said in its report at 7:00 am (1200 GMT).

Elida, which registers maximum sustained winds of 85 kilometers (53 miles) per hour, was bringing heavy rain to seven states along the Pacific coast, including Michoacan, Jalisco and Colima.

Authorities in those states have raised an alert for high winds and strong waves of up to four meters (13 feet).

The slightly weaker Douglas, which is slowly moving away from Mexico, was Tuesday morning 720 kilometers southwest of the resort town of Cabo San Lucas, on Baja California Sur, with sustained winds of 75 kilometers per hour.

The tropical storm has brought downpours and waves up to three meters in Baja California Sur.

Authorities have also warned of the risk of landslides and flooding, cautioning the population to remain alert.

In late May, Amanda, the first hurricane of the 2014 season -- which runs until the end of November -- killed three people in Michoacan and Guerrero states.

Last year, Mexico was hit simultaneously by hurricanes Ingrid in the Gulf of Mexico and Manuel on the Pacific coast, killing 157 people.