The storm is expected to turn westward at that time, the forecast said, well to the north or northeast of the Lesser Antilles through early next week.
Sub-Tropical Storm Oscar is located 1120 miles east-southeast of Bermuda and is moving to the west-northwest at 12 mph (19 km/h).
The Atlantic hurricane season runs from June 1 to November 30 each year, while the Eastern Pacific hurricane season runs from May 15 to November 30, the center said.
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Oscar became the eighth hurricane of the 2018 Atlantic season Sunday but was far out in the Atlantic and posing no threat to land.
The storm had top sustained winds of 70 miles per hour (110 kph).
The Tropical Storm Oscar has got upgraded into a Category 1 hurricane with maximum sustained winds of 120 kmph.
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Subtropical storms have less defined and cooler centres than tropical storms.
Oscar is forecast to continue to strengthen through Monday night, then gradually weaken in the open Atlantic.
The Atlantic hurricane season typically peaks in September and October, but major storms do sometimes form in November.
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