HTTP adaptive streaming technology is now widely adopted in multimedia services because of its ability to provide adaptation to the streaming context, especially characteristics of end-user devices and dynamic network conditions. There are various studies targeting the evaluation of the Quality of Experience (QoE) in this framework. However, none has considered the scenario of the user changing the viewing device during the streaming session, which is the objective of this paper. It provides the following major contributions: definition of the multi-device streaming session scenario; the implementation of a realistic testing case; the execution of subjective tests involving 28 people; and the detailed analysis of the influence of the devices’ switching events.