Results are presented from measurements on internal tides and near-inertial motions, obtained using deep-towed acoustic Doppler current profilers along a single transect over the continental slope in the Bay of Biscay and, in another experiment, over a flank of Great Meteor Seamount in the Canary Basin. Each measurement lasted two days and involved repeated passage of the same track, making it possible to extract by harmonic analysis the semidiurnal (and, over Great Meteor Seamount, also the combined diurnal/near-inertial) signal. In the Bay of Biscay, the transect covered by the towing was sufficiently long to follow the internal semidiurnal tidal beam for large-scale stratification well beyond its detachment from the continental slope. Here, "large-scale" stratification is computed from CTD-observations over vertical scales O(100 m). Remarkably, the beam is much more distinct in its phase field, which is coherent throughout, than in its amplitude, which shows a lot of patchiness and small-scale near-horizontal layering. The hypothesis is put forward that this may be associated with the interaction between internal waves and variations in space and time of stratification. In part, it may be attributable to aliased, weaker, near-inertial beams that are more horizontal for large-scale stratification. The diurnal/inertial and, to a lesser extent, semidiurnal signals over Great Meteor Seamount show the same phenomenon, but here co-phase and coamplitude bands are more distinctly nearly horizontal, indicative of near-horizontal energy propagation at all frequencies investigated.