  The constraints imposed by chiral symmetry on hadron correlation functions in
nuclear medium are discussed. It is shown that these constraints implies the
certain structure of the in-medium hadron correlators and lead to the
cancellation of the order $\rho m_\pi$ term in the in-medium nucleon
correlator. We also consider the effect of mixing of the chiral partners
correlaton 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.
