The instability of normal neutron star matter is investigated from the viewpoint of collective oscillations which are coupled with condensed pions in neutron matter. It is shown that there is no inconsistency between the instability conditions obtained by· two apparently different approaches, i.e., the mean field method by Sawyer et al. and the Green's function method by Migdal. The double pole condition, which determines the instability threshold in the Green's function method, is interpreted in terms of collective motions. §I. Introduction It is of great interest whether or not the pion condensate appears in superdense nuclear matter in connection with the cooling mechanism of neutron stars/> the understanding of transient superdense states caused by high-energy heavy-ion col lisions2> and other related problems. 3) There are two apparently different approach es to the problem of pion condensation in neutron star matter. That is, Sawyer and Scalapino4> h;l.Ve worked the problem on the basis of the Hamiltonian in which the condensed n- field has been replaced by the mean field. A series of their work has indicated the possibility that the ground state of neutron star matter would be rearranged at a slightly greater nucleon density than the normal nuclear matter density p0• Then the new ground state has been prepared to be a coherent mixture of protons, neutrons and condensed negtive pions. In a preceding paper, 5>, we have shown that this state can be treated with the coherent-state representation of proton particle-neutron hole. On the other hand, by using the pion Green's function, Migdal6> has obtained the conclusion that neutral pions would be able to appear at the smaller density than Po and charged pions nearly at the same density. It is the purpose of this paper to reproduce the results of the mean field method and the Green's function method by using the method of normal mode which was introduced by Sawada and Fukuda 7> in order to study the stability of the Hartree-F ock state within the rang~ of the random phase approximation (RP A). They have pointed out that there exists an extremely important relation between the instability of the Hartree-Fock state and the solution of the RPA equation which describes some kind of approximate normal mode. When an infinitesimal