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The IP multimedia subsystem (IMS) is standardized by the 3rd generation partnership project (3GPP) and 3GPP2 as a new core network domain to support Internet Protocol (IP) based multimedia services over 3G networks. Session initiation protocol (SIP) which is an application layer signaling protocol is also standardized by 3GPP and 3GPP2 for session establishment, management, and transformation. In this paper, we study the SIP-based signaling delay for IMS session establishment in 3rd generation (3G) network and worldwide interoperability for microwave access (WiMax) network for different channel rates. In our delay analysis, we take into account transmission, processing and queueing delays at network nodes. The delay analysis of SIP based signaling for IMS provides an insight into the efficiency of SIP signaling for IMS.