Chiral symmetry and properties of hadron correlators in matter

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.