Abstract The collective potential energy of even-even heavy isotopes of fermium is studied. The energy is calculated using the macroscopic-microscopic method. The Yukawa-plus-exponential model is used for the macroscopic part of the energy and the Strutinski shell correction, based on the Woods-Saxon single-particle potential, is taken as the microscopic part. The energy is analyzed in the five-dimensional deformation space, described by the usual deformation parameters: β λ ( λ = 2, 3, 4, 5, 6). The results explain in a natural way the simultaneous appearance of both fission modes (with a low and high total kinetic energy of the fragments), observed recently for 258Fm. The important role of the reflection-asymmetric deformations of the nucleus in this explanation is stressed.