We present a comprehensive study of the effects of third-order dispersion (TOD) on dispersion-managed (DM) solitons. The two main effects of TOD are creation of asymmetry of the DM soliton's profile and generation of continuum radiation. Considering these two effects, we derive a conservative bound on the magnitude of TOD below which it will not have a significant detrimental effect on DM solitons over transoceanic distances. We also calculate the shifts in the DM soliton's position and central frequency that are due to TOD. Finally, we discuss a novel possibility of observing a nonradiating soliton in DM systems with TOD.
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