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At 0300 GMT, Barbara was located around 230 miles (370 kilometers) west of the port of Manzanillo, with maximum sustained winds of 70 miles an hour (110 km/h), the US-based National Hurricane Center (NHC) said.
"Continued weakening is forecast, and the system is forecast to become a remnant low by Wednesday," the NHC said in an advisory.
The agency also warned that swells generated by Barbara would affect parts of the coast of southwestern Mexico during the next day or so. "These swells are likely to cause life-threatening surf and rip current conditions," it predicted.
Mexico's meteorological service earlier warned of heavy rains in coastal areas of the western states of Jalisco, Colima, and Michoacan.
Another storm, named Cosme, was located about 600 miles off the southern tip of the Baja California peninsula, with sustained winds of 70 miles per hour, and was forecast to weaken later Tuesday, according to the NHC.
Hurricanes hit Mexico every year on both its Pacific and Atlantic coasts, usually between May and November.
In October 2023, Hurricane Otis, a scale-topping Category 5 storm, left a trail of destruction and dozens dead after slamming into the Pacific beach resort of Acapulco.