  Recent observations of long and short gamma-ray bursts have revealed a
puzzling X-ray activity that in some cases continues for hours after the burst.
It is difficult to reconcile such time scales with the viscous time scales that
an accretion disk can plausibly provide. Here I discuss the accretion activity
expected from the material that is launched into eccentric, but gravitationally
bound orbits during a compact binary merger coalescence. From a simple
analytical model the time scales and accretion luminosities that result from
fallback in the aftermath of a compact binary merger are derived. For the
considered mass range, double neutron star binaries are relatively homogeneous
in their fallback luminosities. Neutron star black hole systems show a larger
spread in their fallback behaviour. While the model is too simple to make
predictions about the detailed time structure of the fallback, it makes
reasonable predictions about the gross properties of the fallback. About one
hour after the coalescence the fallback accretion luminosity can still be as
large as $\sim 10^{45}$ erg/s, a fraction of which will be transformed into
X-rays. Large-scale amplitude variations in the X-ray luminosities can
plausibly be caused by gravitational fragmentation, which for the
high-eccentricity fallback should occur more easily than in an accretion disk.
