In France, for several years, a number of groups connected with IREM have been considering the potential for teaching secondary mathematics offered by computer algebraic systems (C.A.S.), as well as the problems associated with integrating computer based work into the mathematics curriculum. This research is supported by the National Ministry of Education’s initiative DITEN, which has itself set up a working group. This is by no means an easy task: there is a persistent gap between the discourse and enthusiastic writings of innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching. What exactly are the real potentialities for the use of C.A.S. to support mathematics teaching, and for what level? What conditions favour its use? Where do obstacles lie, and are they located in the hardware or the software, at the cognitive level, in didactic practice, or at the institutional level? With regard to all these questions, our understanding is as yet very limited. In order to make progress we need to begin by collating the work that has already been done on using C.A.S., and to consider innovations that have been introduced. This is the work we have been doing since 1993 in the DIDIREM. group, working in close cooperation with the DITEN group refered to above. In this article I give a brief survey of our work. This is followed by a summary of what the literature claims are the advantages offered by using C.A.S. to teach mathematics. I then present what we have learned from our observations of the teaching sessions we have run, and this leads me to identify a number of points which seem to require particular vigilance on the part of teachers and teacher trainers. (ZDM/Mathdi)