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We propose the network-coding-based relay MAC protocols that aim at providing drive-thru Internet services to the moving vehicles by utilizing the dedicated short range communication (DSRC) over vehicular networks. Our proposed MAC protocols can adaptively switch between two communications modes according to the highway traffic-load conditions. When the highway traffic load is heavy, our system works under the one-hop communications mode. When the density of vehicles on the road is low, the service base station turns on the network-coding-based two-hop relay mode that can extend the coverage of the non-safety data services to the two-hop area. We propose the wireless-network-coding schemes in the relay communications mode to improve the network performance. We also develop the analytical models to analyze the performance of our protocols. Also conducted are simulation experiments to validate and evaluate our proposed MAC protocols. Compared with the traditional IEEE 802.11 MAC protocol for Internet drive-thru services, our proposed relay MAC protocol can significantly increase the network efficiency.