This paper describes an algorithm which supports multimedia service mobility within a Fix/ Mobile Converged Telecommunications Network. A strong focus is given on the support of profile based multimedia service adaptation. The paper also considers the functional architecture of the Next Generation Network (NGN), which is currently being standardized by the International Telecommunication Union (ITU). A short description of a Generic multimedia service architecture Model including QoS aspects (bandwidth, delay, delay variation) is given, followed by a detailed explanation of the required network entities and the algorithm by itself. Different handover scenarios are considered, including devices with network access of different capabilities within different IP domains.