Since the beginning of this century the issue of `quality' has been gaining increasing importance in a number of fields of human activities. For telecommunication services, too, the quality perceived by customers has been taken into account early on as an issue of strategic importance. Whilst for telephony the Quality of Service (QoS) has been already investigated and identified in terms of parameters and related test methodology, the situation for high speed data services (i.e. CBDS/SMDS, Frame Relay, etc.), provided by means of high speed network based on Asynchronous Transfer Moe (ATM) or Metropolitan Area Network technologies, can still be considered `under study'. There is a death of experience not only in terms of measurement instruments and procedures, but also in terms of knowledge of the relationship between the QoS provided at a network level and the quality perceived by the user on his or her terminal. The complexity of the equipment involved in setting up an end-to-end solution based on high speed data communications makes the problems of knowledge and supply of quality very hard to solve. Starting from the experience gained in carrying out high- speed network field trials based on Metropolitan Area Networks and, more recently, on ATM technology, the paper mainly deals with the problem of defining, measuring and then offering a specific QoS. First, the issue of what the user expects from the `high-speed network' is addressed. This analysis is carried out trying to gather what is peculiar to high-speed data communications from the user standpoint. Next, the focus is on how to cope with the requirements due to users' expectations, while carefully considering the basic principles of quality. Finally, a solution is proposed, starting from the experience gained from high speed networks installed in Italy.