  The constraints imposed by chiral symmetry on hadron correlation functions in
nuclear medium are discussed. It is shown that these constraints imply some
structure of the in-medium hadron correlators, lead to the cancellation of the
order $\rho m_\pi$ term in the in-medium nucleon correlator and result in the
effect of mixing of the chiral partners correlators, reflecting the phenomena
of partial restoration of chiral symmetry. The different scenarios of such
restorations are briefly discussed.
