  The cut-off regime of high-order harmonic generation (HHG) by atoms in an
intense laser field is studied numerically and analytically. We find that the
cut-off regime is characterized by equal dephasing between the successive
harmonics. The change of the harmonic phase-locking when HHG evolves from the
cut-off to the plateau regime determines the optimal bandwidth of the spectral
region which should be used for attosecond pulse generation via amplitude
gating technique. The cut-off regime is also characterized by a linear
dependence of the harmonic phase on the fundamental intensity. The
proportionality coefficient grows as the cube of the fundamental wavelength,
thus this dependence becomes very important for the HHG by mid-infrared fields.
Moreover, for every high harmonic there is a {\it range} of laser intensities
providing the generation in the cut-off regime and the atomic response
magnitude in this regime can be greater than that in the plateau regime. Thus
the cut-off regime substantially contributes to the harmonic energy emitted
under typical experimental conditions where the laser intensity varies in time
and space.
