Analytical formulations of the throughput of multi-channel medium access control (MAC) protocols are presented. Both multi-channel multi-rate MAC and multi-channel CoopMAC protocols are considered. A discrete time Markov chain is used to model the number of nodes communicating with the AP in the multi-channel multi-rate MAC protocol, while another discrete time Markov chain is used to model the number of data channels used in the multi-channel CoopMAC protocol. The throughput of the multi-channel multi-rate MAC protocol is expressed as a function of the number of data channels, the channel transmission rate and the solutions to the first Markov chain, while the throughput of the multi-channel CoopMAC protocol is expressed as a function of the number of data channels, the channel transmission rates, and the solutions to the latter Markov chain. The first Markov chain only considers direct one-hop links communications in the multi-channel multi-rate MAC, while the latter Markov chain accounts not only the direct one-hop links communications but also for faster two-hop relaying links communications in the multi-channel CoopMAC as well. Numerical results of the throughput corresponding to typical values are presented. The results also clearly demonstrate the advantage of our proposed multi-channel CoopMAC protocol over a multi-channel multi-rate MAC protocol.