In wireless relay networks (WRNs), multiple source nodes communicate with a single destination node through a common relay network. Different source nodes may have different error protection or recovery time requirements. In this paper, we focus on unequal error protection (UEP) distributed network coding (DNC) design for WRNs. Specifically, we propose a continuous UEP method based on fountain codes with the objective of satisfying the UEP or unequal recovery time (URT) requirements. Then based upon this UEP method, we develop an adaptive UEP DNC scheme to realize adaptive UEP in WRNs. We analyze the properties of the proposed adaptive UEP DNC scheme and derive the upper and lower bit error rate (BER) bounds for it over Rayleigh fading channels under maximum-likelihood (ML) decoding. Simulation results show that the proposed adaptive UEP DNC scheme has desirable UEP and URT properties. The transmitted data from the source nodes in different protection groups can be recovered successfully under their performance requirements in a shorter time by using the adaptive UEP DNC scheme.