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In this paper, we analyze the performance of a nonlinear two-photon-absorption (TPA) receiver and compare its performance with that of a single-photon-absorption (SPA) receiver in the context of spectral-phase-encoded optical code-division multiple access (CDMA) technique. The performances for the above systems are evaluated for two different transmission scenarios, namely, asynchronous and slot-level synchronous transmitters. Performance evaluation includes different sources of degradation such as multiple-access interference, noise due to optical amplification, shot noise, and thermal noise. In obtaining the performance, the mean and variance of the received signal in each of the above techniques are derived, and bit error rate is obtained using Gaussian approximation. In general, it is shown that TPA receivers are superior in performance with respect to SPA receivers when the receiver employs a much slower photodetector in comparison with the laser's transmitted pulse duration. This, indeed, is the reason behind the choice of nonlinear receivers, such as TPA, in most spectral-phase-encoded optical CDMA systems.