When concentrated in mildly acidic solutions, bovine pancreatic ribonuclease (RNase A) forms long-lived oligomers including two types of dimer, two types of trimer, and higher oligomers. In previous crystallographic work, we found that the major dimeric component forms by a swapping of the C-terminal β-strands between the monomers, and that the minor dimeric component forms by swapping the N-terminal α-helices of the monomers. On the basis of these structures, we proposed that a linear RNase A trimer can form from a central molecule that simultaneously swaps its N-terminal helix with a second RNase A molecule and its C-terminal strand with a third molecule. Studies by dissociation are consistent with this model for the major trimeric component: the major trimer dissociates into both the major and the minor dimers, as well as monomers. In contrast, the minor trimer component dissociates into the monomer and the major dimer. This suggests that the minor trimer is cyclic, formed from three monomers that swap their C-terminal β-strands into identical molecules. These conclusions are supported by cross-linking of lysyl residues, showing that the major trimer swaps its N-terminal helix, and the minor trimer does not. We verified by X-ray crystallography the proposed cyclic structure for the minor trimer, with swapping of the C-terminal β-strands. This study thus expands the variety of domain-swapped oligomers by revealing the first example of a protein that can form both a linear and a cyclic domain-swapped oligomer. These structures permit interpretation of the enzymatic activities of the RNase A oligomers on double-stranded RNA.