  In addition to coherent pulsation, many accreting neutron stars exhibit
flaring activity and strong aperiodic variability on time scales similar to or
shorter than their pulsation period. Such a behavior shows that the accretion
flow in the vicinity of the accretor must be highly non-stationary. Although
from the theoretical point of view the problem of non-stationary accretion has
been addressed by many authors, observational study of this phenomenon is often
problematic as it requires very high statistics of X-ray data and a specific
analysis technique. In our research we used high-resolution data taken with
RXTE and INTEGRAL on a sample of bright transient and persistent pulsars, to
perform an in-depth study of their variability on time scales comparable to the
pulsation period - "pulse-to-pulse variability". The high-quality data allowed
us to collect individual pulses of different amplitude and reveal differences
in their spectra (such an analysis we refer to as "pulse-to-pulse
spectroscopy"). The described approach allowed us for the first time to study
luminosity-dependence of pulsars' X-ray spectra in observations where the
averaged (over many pulse cycles) luminosity of the source remained constant
and discuss them in the frame of the current physical models of the accretion
flow close to the neutron star surface.
