The investigation into the relationship between Greek and Babylonian systems of learning has overwhelmingly focused on determining the elements that the former borrowed from the latter, while the fundamental questions relating to the process of transmission of these elements are still largely ignored. This thesis, therefore, offers a preliminary theoretical framework within which the movement of ideas should be analysed. The framework is based on the understanding that all ideas from one culture, when they are to enter another thought and belief system, must be ’translated’ into the concepts and terminology prevalent in their new context. An approach is developed which exploits the concept of ’cultural translation’ as put forward within various modern disciplines. The thesis examines how the ’translatability’ of the material from the perspective of the receiving culture influences its inclusion into the new ’home repertoire’ and determines the changes it undergoes as part of this process. A number of case studies in astronomy, astrology and mathematics are presented to help explain what parts of ’Chaldean knowledge’ were utilised by Greek and Hellenistic scholars, how these were interpreted according to the existing Greek intellectual network into which the new material was inserted and how it was influenced by the ’cultural grid’, a construct reflecting patterns of expectation about a foreign culture.