The hurricane's maximum sustained winds swirled at 75 miles (120 kilometers) per hour about 260 miles north of Bermuda, the US National Hurricane Center said in an 0900 GMT bulletin.
Though the storm remained far from the British overseas territory, "swells from Kate will begin to affect Bermuda this morning and continue through the remainder of today," the NHC said.
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"These swells are likely to cause life-threatening surf and rip current conditions."
Kate, which was moving northeastward at 75 miles per hour, is expected to lose tropical characteristics by Thursday but remain a powerful cyclone during that time.
It is the 11th named storm of the Atlantic hurricane season, which runs through the end of November.
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The most powerful storm of the season so far was Hurricane Joaquin, a Category 4 storm that punished the Bahamas in early October and caused the sinking of a cargo ship with 33 crew members aboard.
Until then, the deadliest was Tropical Storm Erika, which killed 30 people and wreaked extensive damage in the small Caribbean island of Dominica in August.
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