We report an analysis of the magneto-conductance oscillations in two-dimensional mesoscopic ring structures with different geometric symmetry. In particular, we demonstrate that the h/2e magneto-conductance oscillations may be absent or present in purely ballistic quantum rings depending on their geometric symmetry. A detailed analysis of the results is carried out by expanding the transmission amplitudes with backscattering terms. The role of interchannel scattering, which is an essential element of multichannel ballistic transport, is stressed. (C) 2003 Elsevier Ltd. All rights reserved.