We present the results of our detailed calculations of scattering characteristics in e −e +p¯ (e −e +p) and e +e −He++ systems with zero total orbital momentum by direct solving the Faddeev–Merkuriev equations in the differential form. We calculate all possible cross-sections in the low-energy region which admits up to seven open channels including the rearrangement channels of ground and excited states of antihydrogen, positronium and helium ion formations. All sharp resonances of the systems obtained and approved previously by a number of authors are clearly reproduced in the calculated cross sections. Alternatively, the exterior complex scaling approach has been used for calculating resonant energies. It confirmed the existence of reported by other authors broad resonances in the e +e −He++ system. Prominent oscillations of Gailitis–Damburg type have been found in cross sections for energies above the threshold corresponding to n = 2 state of antihydrogen.