Network coding allows a significant increase in throughput in multicast and broadcast scenarios; by letting intermediate nodes between data sources and destinations forward a coded version of incoming packets. Random network coding is a type of network coding in which the coefficients used to encode the data packets are randomly extracted from a Galois field. Hence, it can be used in a network where the network topology is unknown. In a network coded system with practical wireless communication links, a decoding error at the destination may be observed due to linearly dependent coefficient vectors or due to missing packets at the intermediate relays because of fading channel characteristics. Taking these factors into account, in this paper we have analyzed the impact of Rayleigh and Rician fading channels on the performance of a random network coded systems.