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This paper presents performance analysis and cross-layer design approaches for hybrid ARQ (HARQ) protocols in wireless networks, which employ adaptive modulation and coding (AMC) in conjunction with adaptive cooperative diversity and are subject to time-correlated fading channels. We first consider a point-to-point scenario, i.e., non-cooperative HARQ with AMC. Utilizing a Markov channel model which accounts for the temporal correlation in the successive transmission of incremental redundancy by the HARQ protocol, we derive the system throughput and the packet loss probability based on a rate compatible punctured convolutional code family. Next, we consider a cooperative HARQ (CHARQ) scheme in which a relay node, also equipped with AMC, retransmits redundancy packets when it is able to decode the source information packet correctly. For this scenario, we also derive the throughput and packet loss performance. Finally, we present a cross-layer AMC design approach which takes into account the hybrid ARQ protocol at the link layer. The results illustrate that including AMC in the HARQ protocols leads to a substantial throughput gain. While the performance of the AMC with HARQ protocol is strongly affected by the channel correlation, the CHARQ protocol provides noticeable performance gains over correlated fading channels as well.