The birds were swimming near Antrim Marina, at the point where the Six Mile Water enters Lough Neagh.
Officers from the Ulster Society for the Prevention of Cruelty to Animals took one of the swans to a veterinary surgeon in Coleraine, County Londonderry.
The cause of the spillage has not yet been identified.
USPCA Chief Executive Stephen Philpott said the birds must now be rounded up and cleaned as a matter of urgency.
He said it was a worrying situation.
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Swans treated after oil spillage
Animal welfare officers are treating up to 60 swans and their young which have been affected by an oil spillage in County Antrim.
