Fault-tolerant broadcast is a fundamental service in distributed systems, by which processes can communicate with each other consistently and reliably. It has two main forms: Reliable Broadcast (RB) and Uniform Reliable Broadcast (URB). This service has been extensively investigated in non-anonymous distributed systems where processes have unique identifiers, usually assume the communication channels are reliable, which is not always the case in real systems. In this paper, the fault-tolerant broadcast service is studied in an anonymous asynchronous message passing distributed system model with fair lossy communication channels. Firstly, two simple and non-quiescent algorithms implementing RB and URB are given. Secondly, two new classes of failure detectors AΘ and AP∗ are proposed. Finally, with the information provided by AΘ and AP∗ , quiescent algorithms for both RB and URB are given. Categories and Subject Descriptors H.3.4 [System and Software]: Distributed Systems General ...