  Context. The disc instability model (DIM) successfully explains why many
accreting compact binary systems exhibit outbursts, during which their
luminosity increases by orders of magnitude. The DIM correctly predicts which
systems should be transient and works regardless of whether the accretor is a
black hole, a neutron star or a white dwarf. However, it has been known for
some time that the outbursts of X-ray binaries (which contain neutron-star or
black-hole accretors) exhibit hysteresis in the X-ray hardness-intensity
diagram (HID). More recently, it has been shown that the outbursts of accreting
white dwarfs also show hysteresis, but in a diagram combining optical, EUV and
X-ray fluxes.
  Aims. We examine here the nature of the hysteresis observed in cataclysmic
variables and low-mass X-ray binaries.
  Methods. We use the Hameury et al. (1998) code for modelling dwarf nova
outbursts, and construct the hardness intensity diagram as predicted by the
disc instability model.
  Results. We show explicitly that the standard DIM - modified only to account
for disc truncation - can explain the hysteresis observed in accreting white
dwarfs, but cannot explain that observed in X-ray binaries.
  Conclusions. The spectral evidence for the existence of different accretion
regimes / components (disc, corona, jets, etc.) should be based only on
wavebands that are specific to the innermost parts of the discs, i.e. EUV and
X-rays, which is a difficult task because of interstellar absorption. The
existing data, however, indicate that an EUV/X-ray hysteresis is present in SS
Cyg.
