  We identify a new, flux-dependent correction to the antineutrino spectrum as
produced in nuclear reactors. The abundance of certain nuclides, whose decay
chains produce antineutrinos above the threshold for inverse beta decay, has a
nonlinear dependence on the neutron flux, unlike the vast majority of
antineutrino producing nuclides, whose decay rate is directly related to the
fission rate. We have identified four of these so-called nonlinear nuclides and
determined that they result in an antineutrino excess at low-energies below
3.2MeV, dependent on the reactor thermal neutron flux. We develop an analytic
model for the size of the correction and compare it to the results of detailed
reactor simulations for various real existing reactors, spanning 3 orders of
magnitude in neutron flux. In a typical pressurized water reactor the resulting
correction can reach 0.9% of the low energy flux which is comparable in size to
other, known low-energy corrections from spent nuclear fuel and the
non-equilibrium correction. For naval reactors the nonlinear correction may
reach the 10% level.
