In wireless adaptive modulation and coding (AMC) systems, modulation type of a user's connection can change and the ongoing connection might fail due to the change of modulation. In this paper, we approach the AMC-induced call admission control (CAC) problem by focusing on the guaranteed connection. Three classes of calls, new, handoff, and modulation-changed, are considered. We modify the guard-channel CAC scheme such that the modulation-changed calls, in addition to the handoff calls, are allowed to use the guard channel. Then we analyze a Markov model for the CAC scheme designed with long-term AMC in mind. The proposed approach will be an essential tool to determine the guard-channel thresholds in the wireless AMC networks.