In the United Kingdom, as in many other countries, interest is growing rapidly in the nature and capabilities of geographical information systems (GIS). Given the relatively small number of systems currently in use and, in particular, the very restricted number of individuals who have used GIS for a wide range of applications, a conflict of interests arises. It is desirable that education and training are provided on demand and that ad hoc queries are answered: yet the provision for this advice and teaching falls at present upon the most skilled and expert proponents and diminishes their capability to develop or exploit GIS in other ways. The increase in demand for training can, in principle, be satisfied by the creation and use of a computerized tutor which deals with the fundamental concepts of GIS. ARCDEMO is a demonstrator, a primitive tutor, developed to show the capabilities of the ARC/INFO GIS, and its design and implementation arc described. The system contains both text and multicolour graphics, sections of which can be viewed in sequence or selectively from a menu. Operations covered by the demonstrator include: automatic validation and correction of data; change of projection; selective retrieval of spatial data; map overlay; and network analysis. A second demonstrator, called ECDEMO, was developed from the basic structure of ARCDEMO but illustrates an environmental data base established for the European Community. We describe the extent of use and successes and failures of these demonstrators and, on the basis of this experience, we set out desiderata for fully-fledged tutors, suggest the contributions which could be made by knowledge-based systems, outline the machine and human resources needed for running such tutors and conjecture the merits of an international collaborative project to set up a GIS tutor with appropriate national data sets.