  Context: In addition to coherent pulsation, many accreting neutron stars
exhibit flaring activity and strong aperiodic variability on time scales
comparable 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. Observational study of this phenomenon is often problematic as
it requires very high statistics of X-ray data and a specific analysis
technique. Aims: 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". Methods: The high-quality data
allowed us to collect individual pulses of different amplitude and explore
their X-ray spectrum as a function of pulse amplitude. The described approach
allowed us for the first time to study the luminosity-dependence of pulsars'
X-ray spectra in observations where the averaged (over many pulse cycles)
luminosity of the source remains constant. Results: In all studied pulsars we
revealed significant spectral changes as a function of the pulse height both in
the continuum and in the cyclotron absorption features. The sources appear to
form two groups showing different dependencies of the spectrum on pulse height.
We interpret such a division as a manifestation of two distinct accretion
regimes that are at work in different pulsars.
