Nowadays, telecom operators are making a remarkable progress in providing a wide offer of broadband access to answer the high demand for high bit rate applications. Nevertheless, user requirements do not stop at providing high rate connection, but exceeds it to ensuring transparent service portability among his equipments. The user would like to choose among his devices those which respond at best his needs and constraints. From small smart phones to large screen devices, the customer enjoys its entertainments or business meetings according to its current situation. Service continuity over different terminals known as session mobility is a challenging operation in terms of handover latency, context transfer and media adaptation. Moreover, this transfer requires synchronization between the involved terminals. In this paper we present “SESSAMO”, a new lightweight session mobility protocol for streaming applications using RTSP. This solution is transparent to the network and does not require any changes in the client or server streaming application. The solution is detailed and a set of measurement results are presented. In addition, we present a new method to renegotiate session parameters following terminal capacities in order to adapt the flow accordingly. Renegotiation proposal is based on the use of SDPng and MPEG-21