  The equation of state of neutron star matter is examined in terms of the
relativistic mean-field theory, including a scalar-isovector $\delta$-meson
effective field. The constants of the theory are determined numerically so that
the empirically known characteristics of symmetric nuclear matter are
reproduced at the saturation density. The thermodynamic characteristics of both
asymmetric nucleonic matter and $\beta$-equilibrium hadron-electron
$npe$-plasmas are studied. Assuming that the transition to strange quark matter
is an ordinary first-order phase transition described by Maxwell's rule, a
detailed study is made of the variations in the parameters of the phase
transition owing to the presence of a $\delta$-meson field. The quark phase is
described using an improved version of the bag model, in which interactions
between quarks are accounted for in a one-gluon exchange approximation. The
characteristics of the phase transition are determined for various values of
the bag parameter within the range $B\in[60,120]$ $MeV/fm^{3}$ and it is shown
that including a $\delta$-meson field leads to a reduction in the phase
transition pressure $P_{0}$ and in the concentrations $n_{N}$ and $n_{Q}$ at
the phase transition point.
