Abstract: In this paper, we investigate the relationship between the energy efficiency (EE) and the spectral efficiency (SE) in multi-carrier code division access (MC-CDMA) two-hop amplify-and-forward relay systems. We resort to asymptotical analysis with the random matrix theory to derive the closed-form SE-EE relationship when the cooperative relays or distributed relays are considered. We analyze the impact of system parameters on the value of the EE and the SE-EE relationship. Moreover, we study the difference between the SE-and EE-oriented system in using the resources. Finally, we provide simulation results to validate our analytical results. Our studies show that the EE is not a monotonic function of the load factor and the number of relays, so that there is a value of the load factor and the number of relays that can maximize the EE. Moreover, the EE-oriented load factor and the number of relays are always less than or equal to the SE-oriented ones.