This paper is a description of the step-by-step approach to the teaching of simultaneous interpreting that I have adopted at the interpreters' training programs at National Taiwan Normal University (GITI) and Fu Jen Catholic University (GITlS). The complicated task of simultaneous interpretation is broken down into more manageable tasks and introduced to the students in a progressive manner. The tasks are sequenced to allow students to assimilate each skill separately before integration. Such an approach aims to prevent tudents from being traumatized by their first experience in the simultaneous interpretation booth.