'Non-western history' nowadays is definitely on the agenda in western historiography. Nevertheless, there are some misunderstandings about the terminology used. In this contributions three meanings of the term are distinguished: 1) traditional colonial historiography in a new vein (which still very often is Eurocentric); 2) the writing of history in non-western countries, using western scientific methods and 3) non-western historiography, that does not meet the requirements of western scientific standards. The author suggests that this last variety of historiography is grossly underestimated and might be particularly interesting, because it sheds light on a few problems in western scientific historiography. Of course, it is impossible to transfer concepts from one cultural setting to another, but they may produce some insight. The article concentrates on four items: oral tradition, the objectivity problem, the concept of time and finally the complex question of presentation and narrativity.