Underwater acoustic communications (UAC) feature frequency-dependent signal attenuation, long propagation delay and doubly-selective fading. Thus the design of reliable UAC protocols is challenging. On the other hand, cooperative relay communications, which have been extensively studied in terrestrial environments, are promising paradigms for reliable communications. However, their application to UAC has not been thoroughly explored. In this study, the authors will design an asynchronous relaying protocol to achieve reliable underwater communications. This new scheme accounts for and takes advantage of the unique characteristics of UAC channels. To avoid time synchronisation difficulty in UAC, and facilitate energy-efficient relay processing, asynchronous amplify-and-forward relaying is adopted in the protocol. In addition, precoded orthogonal frequency division multiplexing is chosen to address the frequency selectivity issue in UAC, while collecting ample multipath diversity provided by the channel and enabled by the asynchronous relaying design. To demonstrate the performance of the protocol, the end-to-end signalto-noise ratio is derived, the average pair-wise error probability is evaluated and the maximum collectable diversity is also proven. Simulations and comparisons are presented to corroborate the analyses and design.