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We introduce an analytical method that uses a finite-state Markov chain (FSMC) as an error model, for estimating the performance of adaptive modulation systems (AMSs) combined with automatic repeat request (ARQ) schemes in correlated slow fading channels. For the throughput performance evaluation of wireless packet networks, conventionally, we have assumed independent block fading, which may also be suitable to represent fast fading channels. However, in slow fading channels, error rates of consecutive packets are highly correlated and we cannot simply assume independent error structure in performance evaluations. We propose a multistate Markov error structure for AMS in correlated fading channels, which is also described by a finite-state Markov chain (FSMC) and we also present throughput-estimation methods for AMS combined with ARQ, using the proposed Markov error structure.