Ballistic electron transport in Aharonov-Bohm-type ring structures is investigated where the single-channel problem is nontrivially extended to the multichannel one in which the important interchannel scattering effect is considered. It is found that the S-matrix of a ring structure should reflect the geometric symmetry if the interchannel scattering effect is properly accounted for and that the symmetry relationships of the S-matrix plays a crucial role in the conductance oscillation behavior in ballistic two-dimensional rings. The magnetostatic as well as the electrostatic Aharonov-Bohm effects are studied for two ring structures of different symmetry. (C) 1998 Academic Press Limited.