Evidence is presented indicating that the stereochemistry of the Stevens rearrangement of the axially chiral onium salts 1a-d and 5 is dramatically structure-dependent. Thus, the binaphthyl ammonium salts (S)-(+)-1a-c react with a strong base with exclusive (100% de) formation of the corresponding rearranged amines (R,3R)-(+)-2a-c, demonstrating a complete transfer of the (S) axial dissymmetry/asymmetry into (R) asymmetry of the newly formed carbon center. Exactly opposite stereochemistry was established in an earlier study by Mislow of the biphenyl analogue (S)-(+)-5, yielding the rearranged products (S,9S)-(+)-6 and (R,9S)-(-)-7 with exclusive (S) configuration at the carbon center. Rearrangement of the sulfonium salt 1d is found to be intermediate between the two extremes, yielding a mixture of diastereoisomeric products 2d and 3d, which differ in configuration at the asymmetric carbon center. A direct proof is thus provided that two stereochemically different pathways can participate in the Stevens rearrangement. An explanation is suggested in terms of competition between suprafacial (concerted) and antarafacial (nonconcerted) mechanism.