The National Meteorological Service issued a forecast at 7:00am for intense storm conditions in Nayarit, Jalisco, Michoacán, Colima, Puebla, Chiapas and Oaxaca.
"Swells generated by Bud will continue to affect portions of the coast of southwestern Mexico during the next few days", the NHC said.
NHC forecasters said: "Maximum sustained winds have increased to near 115 miles per hour (185 km/h) with higher gusts".
At Category 3, Bud was classified as a major hurricane.
Some additional strengthening is possible today but a slow weakening should begin tomorrow. According to the NHC, Hurricane Bud is expected to move north-northwest on Tuesday into the midweek. Rainfall of 3 to 6 inches (75 to 150 millimeters), with isolated patches of 10 inches (250 millimeters), was possible into Tuesday afternoon.
Aletta was the first hurricane of the season and went from a tropical storm to category 4 hurricane in just 24 hours last week but it too was located well away from the coast.
A tropical disturbance in the southern Caribbean has a low chance of developing into a tropical depression or tropical storm.
Satellite view of the Gulf of Mexico.
Up to nine hurricanes and four "major" depressions with sustained winds of at least 100mph have been predicted by United States government, The National Oceanic and Atmospheric Administration (NOAA).
Hurricane forecasters are watching another blob of showers and thunderstorms in what's turning out to be a messy start to the Atlantic hurricane season.
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