Propagation of energy along the sound channel axis cannot be formally described in terms of geometrical acoustics due to repeated cusped caustics along the axis. In neighborhoods of these cusped caustics, a very complicated interference pattern is observed. Neighborhoods of interference grow with range and overlap at long ranges. This results in the formation of a complex interference wave--the axial wave--that propagates along the sound channel axis like a wave belonging to a crescendo of near-axial arrivals. The principal properties of this wave are calculated for the actual space-time configuration realized during a 2004 long-range propagation experiment conducted in the North Pacific. The experiment used M-sequences at 68.2 and 75 Hz, transmitter depths from 350 to 800 m, and ranges from 50 to 3200 km. Calculations show that the axial wave would be detectable for an optimal geometry-both transmitter and receiver at the sound channel axis--for a "smooth" range-dependent sound speed field. The addition of sound speed perturbations--induced here by simulated internal waves--randomizes the acoustic field to the extent that the axial wave becomes undetectable. These results should be typical for mid-latitude oceans with similar curvatures about the sound speed minimum.