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Petrol stations in the area are already being hit by the Shell tanker drivers strike which began this morning.
The Esso service station at Wincheap put up No Fuel signs last night.
And the manager of the Shell Lychgate Service Station on the Thanet Way thinks they will only have petrol for the next two days.
He added: "After that we're going to open but only the shop, no fuel."
The Shell garage at New Romney said they only expect to last the rest of the day.
But there is no need to panic as, according to other petrol stations, there's plenty to go around until Tuesday.
Craig Ellis, manager of Herne Bay's Richmond Service Station, said they had plenty of supplies.
He said: "We're doing fine. we had a tanker in yesterday evening and we've got another one on Sunday which I expect no problems in receiving, so we've got lots of fuel.
"There's no need to panic buy at all."
Drivers from companies that supply petrol to Shell are striking over the soaring prices of fuel and a new pay deal.
The strike is set to last for four days.