We analyze the spectral efficiency (sum-rate per subcarrier) of randomly spread synchronous multicarrier code-division multiple access (MC-CDMA) subject to frequency-selective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio. Both uplink and downlink are considered, either conditioned on the subcarrier fading coefficients (for nonergodic channels) or unconditioned thereon (for ergodic channels). The following receivers are analyzed: a) jointly optimum receiver, b) linear minimum mean-square error (MMSE) receiver, c) decorrelator, and d) single-user matched filter.