  We study the influence of a high density behaviour of the nuclear symmetry
energy on a kaon condensation in neutron stars. We find that the symmetry
energy typical for several realistic nuclear potentials, which decreases at
high densities, inhibits kaon condensation for weaker kaon-nucleon couplings.
There exists a threshold coupling above which the kaon condensate forms at
densities exceeding some critical value. This is in contrast to the case of
rising symmetry energy, as e.g. for relativistic mean field models, when the
kaon condensate can form for any coupling at a sufficiently high density.
Properties of the condensate are also different in both cases.
