  We argue that the effective pion mass in nuclear matter obtained from chiral
effective lagrangians is unique and does not depend on off-mass-shell
extensions of the pion fields as e.g. the PCAC choice. The effective pion mass
in isospin symmetric nuclear matter is predicted to increase slightly with
increasing nuclear density, whereas the effective time-like pion decay constant
and the magnitude of the density-dependent quark condensate decrease
appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other
in-medium identities are studied in addition. Finally, several constraints on
effective lagrangians for the description of the pion propagation in isospin
symmetric, isotropic and homogenous nuclear matter are discussed. (Talk
presented at the workshop ``Hirschegg '95: Hadrons in Nuclear Matter'',
Hirschegg, Kleinwalsertal, Austria, January 16-21, 1995)
