Anytime codes are known to be useful for tracking and controlling unstable systems over noisy channels. Although practical anytime codes have been developed for point-to-point communication, to date no practical code constructions and tractable analysis of anytime codes are known to exist for relay networks. In this paper, we study the design and theoretical analysis of anytime codes for a three-terminal relay network. We propose bilayer codes for anytime transmission over the relay network and consider two transmission schemes for the relay-destination link. For both schemes, we analytically derive the delay-exponents and show that they closely match the corresponding numerical results obtained from density evolution. Through simulation, we also show the finite-length performance of the proposed bilayer anytime code.