"By Tuesday, Oscar is forecast to begin moving to the north or northeast with an increase in forward speed".
But Oscar is no threat to the USA and was deep in the Atlantic as of Sunday morning.
It had 75 mph maximum sustained winds that extended outward only 15 miles.
Hurricane Oscar is now the eighth hurricane in the 2018 Atlantic hurricane season.
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The storm was moving to the west-northwest at 7 miles per hour (11 kph).
The estimated minimum central pressure is 995 mb (29.39 inches). "On a rare occasion, storms that form near the Central America coast can track north into the Gulf of Mexico and turn to the northeast toward Florida", it stated.
Oscar has transitioned from a subtropical storm into a tropical storm and now may become a hurricane soon. The storm is continuing to transition from a hybrid storm to a full-fledged tropical system on Saturday night.
However the storm is not a threat to the island, according to the Bermuda Weather Service. Hurricane season runs through November 30.