  The potential splitting approach incorporated into the framework of
Faddeev-Merkuriev equations in the differential form is used for calculations
of multichannel scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$
systems. Detailed calculations of all possible S-wave cross-sections are
performed %in systems $e^+e^-\bar{p}$ and $e^+e^-\mbox{He}^{++}$ in the
low-energy region which supports up to seven open channels including the
rearrangement channels of ground and excited states of antihydrogen,
positronium and helium ion formations. All known sharp resonances of the
systems obtained and approved by a number of authors are clearly reproduced in
the calculated cross sections. In cross sections for energies above the
threshold corresponding to $n=2$ state of antihydrogen the prominent
oscillations of Gailitis Damburg type have been found.
