  The constraints imposed by chiral symmetry on hadron correlation functions in
nuclear medium are discussed. It is shown that these constraints imply a
certain structure for the in-medium hadron correlators and lead to the
cancelation of the order $\rho m_\pi$ term in the in-medium nucleon correlator.
We also consider the effect of mixing of the chiral partners correlation
functions arising from the interaction of nuclear pions with corresponding
interpolating currents. It reflects the phenomena of partial restoration of
chiral symmetry. The different scenarios of such restoration are briefly
discussed.
