  We present approximate formulae describing the changes in neutron star
parameters caused by the first-order phase transition to an ``exotic'' state
(pion or kaon condensate, quark matter) resulting in formation of a mixed-phase
core. The analytical formulae for the changes in radius, moment of inertia and
the amount of energy released during the core-quake are derived using the
theory of linear response of stellar structure to the core transformation.
Numerical coefficients in these formulae are obtained for two realistic EOSs of
dense matter. The problem of nucleation of the exotic phase as well as possible
astrophysical scenarios leading to a core-quake phenomenon is also discussed.
