Numbering and addressing issues arising in the Integrated Broadband Communication Network (IBCN) for the support of the Universal Mobile Telecommunication System (UMTS) and Personal Telecommunication Service (PTS) are dealt with in this paper. Mobile communications services will allow a user to roam within a network. Thus there will be a need to identify several types of objects (terminals, network points of attachment, users, Customer Premises Networks, etc.). The mobility properties of these objects will necessitate dynamic bindings between their addresses and names. Moreover, the situation is further complicated since the mobility may be embedded. A mobile user may employ a mobile terminal in a mobile Customer Premises Network (CPN). Therefore, in UMTS and PTS there is a need for dynamic binding of various identifiers with location information data. The exclusive use of Personal Telecommunication Numbers (PTN's) as Dialing Numbers (DN) is proposed in IBCN for UMTS and PTS. That is, PTN's will be used (during dialing) for making calls to mobile terminals, mobile users, as well as fixed subscribers. When the personal communication service is not provided, the DN corresponds to the terminal number of the equipment (fixed or mobile) of the called subscriber. Also, a proposal for the UMTS and PTS numbering plan is presented