To better represent fine structure cues in cochlear implants (CIs), recent research has proposed varying the stimulation rate based on slowly varying frequency modulation (FM) information. The present study investigated the abilities of CI users to detect FM with simultaneous amplitude modulation (AM). FM detection thresholds (FMDTs) for 10-Hz sinusoidal FM and upward frequency sweeps were measured as a function of standard frequency (75-1000 Hz). Three AM conditions were tested, including (1) No AM, (2) 20-Hz Sinusoidal AM (SAM) with modulation depths of 10%, 20%, or 30%, and (3) Noise AM (NAM), in which the amplitude was randomly and uniformly varied over a range of 1, 2, or 3 dB, relative to the reference amplitude. Results showed that FMDTs worsened with increasing standard frequencies, and were lower for sinusoidal FM than for upward frequency sweeps. Simultaneous AM significantly interfered with FM detection; FMDTs were significantly poorer with simultaneous NAM than with SAM. Besides, sinusoidal FMDTs significantly worsened when the starting phase of simultaneous SAM was randomized. These results suggest that FM and AM in CI partly share a common loudness-based coding mechanism and the feasibility of "FM+AM" strategies for CI speech processing may be limited.