  We discuss the nature of the kaon condensation phase transition. We find
several features which, if kaons condense in neutron stars, are not only
remarkable, but must surely effect such properties as superfluidity and
transport properties, which in turn are relevant to the glitch phenomenon and
cooling rates of neutron stars. The mixed phase, because of the extensive
pressure range that it spans, will occupy a broad radial extent in a neutron
star. This region is permeated with microscopic drops (and other
configurations) located at lattice sites of one phase immersed in the
background of the other phase. The electric charge on drops is opposite to that
of the background phase {\sl and} nucleons have a mass approximately a factor
two different depending on whether they are in the drops or the background
phase. A large part of the stellar interior has this highly non-homogeneous
structure.
