In this letter, we present the impact of carrier frequency offset (CFO) in dual-hop orthogonal frequency division multiplexing (OFDM) systems with a fixed relay for frequency-selective fading channels. Approximate expressions of the average signal-to-noise ratios (SNRs) for both downlink and uplink are obtained and validated by simulations. It is shown that dual-hop systems have slightly worse average SNR degradation than single-hop systems. We also show that the average SNR degradation due to the CFO varies according to the gap between average received SNRs for the first and the second hop.