The Internet evolution delineated through the last years has urged the wireless network community to support the deployment of IP multimedia services with guaranteed quality of service (QoS) in 3G wireless networks. This article copes with the interoperability between 3G wireless networks and wired next-generation IP networks, for the provision of services with an a priori known quality level over both environments. More specifically, the UMTS architecture as well as a prototypical implementation of the next-generation Internet based on DiffServ are considered. The article focuses on the mapping among the traffic classes of the two networks at the point where the networks converge, and discusses the requirements and possible solutions for their proper interworking at the signaling and user levels. Simulations prove that proper mapping among the traffic classes of each world is necessary in order to achieve the desired end-to-end traffic characteristics.