Payment channel networks (PCNs) enhance the scalability of blockchains by allowing parties to conduct transactions off-chain, i.e, without broadcasting every transaction to all blockchain participants. To conduct transactions, a sender and a receiver can either establish a direct payment channel with a funding blockchain transaction or leverage existing channels in a multi-hop payment. The security of PCNs usually relies on the synchrony of the underlying blockchain, i.e., evidence of misbehavior needs to be published on the blockchain within a time limit. Alternative payment channel proposals that do not require blockchain synchrony rely on quorum certificates and use a committee to register the transactions of a channel. However, these proposals do not support multi-hop payments, a limitation we aim to overcome. In this paper, we demonstrate that it is in fact impossible to design a multi-hop payment protocol with both network asynchrony and faulty channels, i.e., channels that may not correctly follow the protocol. We then detail two committee-based multi-hop payment protocols that respectively assume synchronous communications and possibly faulty channels, or asynchronous communication and correct channels. The first protocol relies on possibly faulty committees instead of the blockchain to resolve channel disputes, and enforces privacy properties within a synchronous network. The second one relies on committees that contain at most f faulty members out of 3f+1 and successively delegate to each other the role of eventually completing a multi-hop payment. We show that both protocols satisfy the security requirements of a multi-hop payment and compare their communication complexity and latency.