  We investigate the properties of different modifications to the linear
$\sigma$-model (including a dilaton field associated with broken scale
invariance) at finite baryon density $\rho$ and nonzero temperature $T$. The
explicit breaking of chiral symmetry and the way the vector meson mass is
generated are significant for the appearance of a phase of nearly vanishing
nucleon mass besides the solution describing normal nuclear matter. The
elimination of the abnormal solution prohibits the onset of a chiral phase
transition but allows to lower the compressibility to a reasonable range. The
repulsive contributions from the vector mesons are responsible for the wide
range of stability of the normal phase in the $(\mu,T)$-plane. The abnormal
solution becomes not only energetically preferable to the normal state at high
temperature or density, but also mechanically stable due to the inclusion of
dilatons.
