Cochlear-implant speech processors transmit temporal features of sound as amplitude modulation of constant-rate electrical pulse trains. The present study evaluated the central representation of amplitude modulation in the form of phase-locked firing of neurons in the auditory cortex. Anesthetized pigmented guinea pigs were implanted with cochlear electrode arrays. Stimuli were 254 pulse/s (pps) trains of biphasic electrical pulses, sinusoidally modulated with frequencies of 10 to 64 Hz and modulation depths of -40 to -5 dB re 100% (i.e., 1 to 56.2% modulation). Single- and multi-unit activity was recorded from multi-site silicon-substrate probes. The maximum frequency for significant phase locking ("limiting modulation frequency") was 60 Hz for 42% of recording sites, whereas phase locking to pulses of unmodulated pulse trains rarely exceeded 30 pps. The strength of phase locking to frequencies 40 Hz often varied non-monotonically with modulation depth, commonly peaking at modulation depths around -15 to -10 dB. Cortical phase locking coded modulation frequency reliably, whereas a putative rate code for frequency was confounded by rate changes with modulation depth. Group delay computed from the slope of mean phase versus modulation frequency tended to increase with decreasing limiting modulation frequency. Neurons in cortical extra-granular layers had lower limiting modulation frequencies than did neurons in thalamic afferent layers. Those observations suggest that the low-pass characteristic of cortical phase locking results from intra-cortical filtering mechanisms. The results demonstrate that cortical neurons can phase lock to modulated electrical pulse trains across the range of modulation frequencies and depths presented by cochlear-implant speech processors.