This paper analyzes the impact on the stability of the TCP-Reno congestion control mechanism when a network coding (NC) layer is inserted in the TCP/IP stack. A model of the dynamics of the TCP-NC protocol combined with random early detection (RED) as active queue management mechanism is considered to study the network equilibrium and stability properties. The existence and uniqueness of an equilibrium point is demonstrated and characterized in terms of average throughput, loss rate, and queue length. Global stability is proved in absence of forward delay, and the effects of the NC redundancy factor and of the delay on the local stability of TCP-NC-RED are studied around the equilibrium. The fairness of TCP-NC with respect to TCP-Reno-like protocols is also studied. A version of TCP-NC with adaptive redundancy factor (TCP-NCAR) is also introduced. Results provided by the proposed model are compared with those obtained by simulation for N sources sharing a single link. TCP-NC-RED becomes unstable when delay or capacity increases, as TCP-Reno does, but also when the redundancy factor increases. Its stability region is characterized as a function of the redundancy factor. If TCP-NC and TCP-Reno share the same links, TCP-NC is fair with TCP-Reno-like protocols when no redundancy is added. Simulations show that TCP-NCAR is able to compensate losses on the wireless parts of the network.