  The relation between the effective chiral Lagrangian whose parameters scale
according to Brown and Rho scaling("BR scaling") and Landau Fermi-liquid theory
for hadronic matter is discussed in order to make a basis to describe the
fluctuations under the extreme condition relevant to neutron stars. It is
suggested that BR scaling gives the background around which the fluctuations
are weak. A simple model with BR-scaled parameters is constructed and
reproduces the properties of the nuclear ground state at normal nuclear matter
density successfully. It shows that the tree level in the model Lagrangian is
enough to describe the fluctuations around BR-scaled background. The model
Lagrangian is consistent thermodynamically and reproduces relativistic Landau
Fermi-liquid properties. Such points are important for dealing with hadronic
matter under extreme condition. On the other hand it is shown that the vector
current obtained from the chiral Lagrangian is the same as that obtained from
Landau-Migdal approach. We can determine the Landau parameter in terms of
BR-scaled parameter. However these two approaches provide different results,
when applied to the axial charge. The numerical difference is small. It shows
that the axial response is not included properly in the Landau-Migdal approach.
