A medieval tradition alleges that the various branches of the Fleming family of the British Isles are descended from the three sons of an earl of Flanders. Pitted against this tradition is the more recent allegation, first made no earlier than the eighteenth century, that unrelated families immigrated in the twelfth and thirteenth centuries to the British Isles from Flanders and independently chose Fleming as a surname. What do historical records have to say concerning these two opposing views? In this publication it is asserted that the records are unanimously in favour of ancient tradition and that the modern allegation is nonsense. The traditional "earl of Flanders" was in reality a man named Erkenbald, the son of an exiled Flemish nobleman living in Normandy during the first half of the eleventh century. Erkenbald the Fleming came to England with William the Conqueror in 1066, and through him are the Flemings of the British Isles descended from one of the great noble houses of Flanders.