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3GPP-LTE networks use the EAP-AKA protocol to authenticate and negotiate session keys with mobile users. However, with the popular trend of single user owning multiple devices and subscribing to multiple services, the EAP-AKA protocol appears inefficient because its authentication is device-oriented. In this paper, we propose a secure and efficient multi-device and multi-service authentication protocol, called SEMMAP, for 3GPP-LTE networks. SEMMAP makes use of a key hierarchy and an authority-issued license to enable an authenticating server to quickly verify the legitimacy of multiple devices belonging to the same mobile user and conduct a fast key negotiation between the server and the mobile user. Performance analysis shows that SEMMAP is more efficient than the current EAP-AKA protocol under the multi-device, multi-service scenario in terms of authentication delay and storage overhead for Authentication Vector (AV) at authenticating servers.