  We study possible impact of a softening of the equation of state by a phase
transition, or appearance of hyperons, on the spin evolution of of isolated
pulsars. Numerical simulations are performed using exact 2-D simulations in
general relativity. The equation of state of dense matter at supranuclear
densities is poorly known. Therefore, the accent is put on the general
correlations between evolution and equation of state, and mathematical
strictness. General conjectures referring to the structure of the one-parameter
families of stationary configurations are formulated. The interplay of the back
bending phenomenon and stability with respect to axisymmetric perturbations is
described. Changes of pulsar parameters in a corequake following instability
are discussed, for a broad choice of phase transitions predicted by different
theories of dense matter. The energy release in a corequake, at a given initial
pressure, is shown to be independent of the angular momentum of collapsing
configuration. This result holds for various types of phases transition, with
and without metastability. We critically review observations of pulsars that
could be relevant for the detection of the signatures of the phase transition
in neutron star cores.
