First order Bose condensation in asymmetric nuclear matter and in neutron stars is studied, with particular reference to kaon condensation. We demonstrate explicitly why the Maxwell construction fails to assure equilibrium in multicomponent substances. Gibbs conditions and conservation laws require that for phase equilibrium, the charge density must have opposite sign in the two phases of isospin asymmetric nuclear matter. The mixed phase will therefore form a Coulomb lattice with the rare phase occupying lattice sites in the dominant phase. Moreover, the kaon condensed phase differs from the normal phase, not by the mere presence of kaons in the first, but also by a difference in the nucleon effective masses. The mixed phase region, which occupies a large radial extent amounting to some kilometers in our model neutron stars, is thus highly heterogeneous. It should be particularly interesting in connection with the pulsar glitch phenomenon as well as transport properties.

25 pagees, 20 figures, Latex