We have measured the mass and kinetic-energy distributions from the spontaneous fission of

{}^{258}{Fm}

{}^{258}{No}

{}^{259}{Md}

{}^{260}{Md}

, and

{}^{260}]

. All are observed to fission with a symmetrical division of mass. The total-kinetic-energy distributions strongly deviated from the Gaussian shape characteristically found in the fission of all other actinides. When the total-kinetic-energy distributions are resolved into two Gaussians, the constituent peaks lie near 200 and 233 MeV. We conclude that both low- and high-energy fission modes occur in four of the five nuclides studied. We call this property ‘‘bimodal fission.’’ Even though both modes are possible in the same nuclide, one generally predominates. We offer an explanation for each mode based on shell structures of the fissioning nucleus and of its fragments. The appearance of both modes of fission in this region of the nuclide chart seems to be a coincidence in that the opportunity to divide into near doubly magic Sn fragments occurs in the same region where the second fission barrier is expected to drop in energy below the ground state of the fissioning nucleus. Appropriate paths on the potential-energy surface of deformation have been found by theorists, but no physical grounds have been advanced that would allow the near equal populations we observe traveling each path. We suggest that this failure to find a reason for somewhat equal branching may be a fundamental flaw of current fission models. Assuming the proposed origins of these modes are correct, we conclude the low-energy, but also mass-symmetrical mode is likely to extend to far heavier nuclei. The high-energy mode will be restricted to a smaller region, a realm of nuclei defined by the proximity of the fragments to the strong neutron and proton shells in

{}^{132}{Sn}

. We present some concluding remarks on the present state of fission theory and indicate a potential redirection that might be taken.

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