  The effect of the hyperon softening of the equation of state (EOS) of dense
matter on the spin evolution of isolated neutron stars is studied for a broad
set of hyperonic EOSs. We use a multidomain 2-D code based on a spectral
method, and show how important the precision of solving the equations of
stationary motion is for the stability analysis. For some EOSs, the hyperon
softening leads to spin-up by the angular momentum loss, in the form of the
back bending phenomenon, for a rather broad range of stellar baryon mass. We
show that large segments of the evolutionary tracks exhibiting the back bending
behaviour in the moment-of-inertia - rotation-frequency plane, are actually
unstable and therefore not astrophysically relevant. We show also that during
the spin-up - angular-momentum-loss epoch, an isolated neutron star (e.g., a
radio pulsar) can lose a sizable part of its initial angular momentum without
significantly changing its rotation period. We propose also simple arguments
and criteria allowing to connect the presence of a back bending epoch with the
mass-radius relations and the stiffness and/or softness of the nucleon and
hyperon EOSs of the neutron star core.
