This letter presents an analysis of asynchronous multicarrier code-division multiple-access (MC-CDMA) systems with a guard period (GP) in the form of a cyclic prefix over frequency-selective multipath fading channels, which results in closed-form bit-error rate performance. Furthermore, it confirms that the frequency diversity of MC-CDMA systems is identical to the path diversity. The analytical approach proposed here is extended to the case without a GP. The derived analytical results show that a GP is required for MC-CDMA systems in order to mitigate not only the effect of intersymbol interference and intercarrier interference, but also the desired signal power degradation.