  Tens of early type galaxies have been recently reported to possess prolate
rotation, i.e. significant amount of rotation around the major axis, including
two cases in the Local Group. Although expected theoretically, this phenomenon
is rarely observed and remains elusive. In order to explore its origin we study
the population of well-resolved galaxies in the Illustris cosmological
simulation. We identify 59 convincing examples of prolate rotators at the
present time, more frequently among more massive galaxies, with the number
varying very little with redshift. We follow their evolution back in time using
the main progenitor branch galaxies of the Illustris merger trees. We find that
the emergence of prolate rotation is strongly correlated with the time of the
last significant merger the galaxy experienced, although other evolutionary
paths leading to prolate rotation are also possible. The transition to prolate
rotation most often happens around the same time as the transition to prolate
shape of the stellar component. The mergers leading to prolate rotation have
slightly more radial orbits, higher mass ratios, and occur at more recent times
than mergers in the reference sample of twin galaxies we construct for
comparison. However, they cover a wide range of initial conditions in terms of
the mass ratio, merger time, radiality of the progenitor orbits, and the
relative orientations of spins of the progenitors with respect to the orbital
angular momenta. About half of our sample of prolate rotators were created
during gas-rich mergers and the newly formed stars usually support prolate
rotation.
