This paper proposes and theoretically evaluates two different schemes of code acquisition for pulse-position modulation (PPM) and overlapping PPM (OPPM) fiber-optic code-division multiple-access (CDMA) systems, namely threshold-based and demodulator-based code acquisition. Single-dwell detector and serial-search algorithm are employed for both schemes. Theoretical analysis is carried out for shot-noise-limited photon-counting receiver. Discussions upon effects of various parameter settings on the performance of code acquisition for PPM/OPPM fiber-optic CDMA systems, such as index of overlap, PPM/OPPM multiplicity, average photon counts per information nat, and darkcurrents, are presented. It is shown that when the threshold is properly selected, the threshold-based code acquisition system offers better performance, in terms of mean number of training frames, than the demodulator-based one.