  The variational principle for stars with a phase transition has been
investigated. The term outside the integral in the expression for the second
variation of the total energy of a star is shown to be obtained by passage to
the limit from the integration over the region of mixed states in the star. The
form of the trial functions ensuring this passage has been found. All of the
results have been generalized to the case where general relativity is
applicable. The known criteria for the dynamical stability of a star when a new
phase appears at its center are shown to follow automatically from the
variational principle. Numerical calculations of hydrostatically equilibrium
models for hybrid stars with a phase transition have been performed. The form
of the trial functions for the second variation of the total energy of a star
that describes almost exactly the stability boundaries of such stellar models
is proposed.
