The effects of a combination of sound‐speed and current fluctuations on propagation of a cw signal in a deep‐ocean model are analyzed. The mean sound‐speed structure is assumed bilinear, and the channel boundaries are horizontal. The horizontally independent sound speed oscillates with a 12‐h period, while the spatially uniform currents consist of quasisteady and diurnally varying components. The total acoustic field for surface‐reflected–bottom‐reflected rays is investigated for dependence on time, source‐receiver separation, and environmental parameters. Multipath propagation is demonstrated for larger propagation ranges, for which case the number, depths, and occurrence times of amplitude fades are shown to be very sensitive to parameter changes. Where the total field is dominated by one ray, contributions from combined sound‐speed and current fluctuations to phase are investigated. In both cases, phase generally can be influenced by both sound‐speed and current fluctuations, but the former more effectively influence amplitude.