In this paper, novel cooperative automatic repeat request (ARQ) methods with network coding are proposed for two way relaying network. Upon a failed transmission of a packet, the network enters cooperation phase, where the retransmission of the packets is aided by the relay node. The proposed approach integrates network coding into cooperative ARQ, aiming to improve the network throughput by reducing the number of retransmissions. For successive retransmission, three different methods for choosing the retransmitting node are considered. The throughput of the methods are analyzed and compared. The analysis is based on binary Markov channel which takes the correlation of the channel coefficients in time into account. Analytical results show that the proposed use of network coding result in throughput performance superior to traditional ARQ and cooperative ARQ without network coding. It is also observed that correlation can have significant effect on the performance of the proposed cooperative network coded ARQ approach. In particular the proposed approach is advantageous for slow to moderately fast fading channels.