This paper studies dual-hop amplify-and-forward relaying system employing differential encoding and decoding over time-varying Rayleigh fading channels. First, the convectional "two-symbol" differential detection (CDD) is theoretically analysed in terms of the bit-error-rate (BER). The obtained analysis clearly shows that performance of two-symbol differential detection severely degrades in fast-fading channels and reaches an irreducible error floor at high signal-to-noise ratio region. To overcome the error floor experienced with fast-fading, a practical suboptimal "multiple-symbol" detection (MSD) is designed and its performance is theoretically analysed. The analysis of CDD and MSD are verified and illustrated with simulation results under different fading scenarios. Specifically, the obtained results show that the proposed MSD can significantly improve the system performance in fast-fading channels.