  Kaon excitations (kaonic modes) are investigated in hyperonic matter, where
hyperons ($\Lambda$, $\Sigma^-$, $\Xi^-$) are mixed in the ground state of
neutron-star matter. $P$-wave kaon-baryon interactions as well as the s-wave
interactions are taken into account within chiral effective Lagrangian, and the
nonrelativistic effective baryon-baryon interactions are incorporated. When the
hyperon $\Lambda$ is more abundant than the proton at high baryon density, a
proton-particle-$\Lambda$-hole mode, which has the $K^+$ quantum number,
appears in addition to other particle-hole modes with the $K^-$ quantum number.
It is shown that the system becomes unstable with respect to a spontaneous
creation of a pair of the particle-hole modes with $K^+$ and $K^-$ quantum
numbers, stemming from the p-wave kaon-baryon interaction. The onset density of
this p-wave kaon condensation may be lower than that of the s-wave $K^-$
condensation.
