[en] We investigate the condensation of charged K^- meson and neutral anti-K⁰ meson in dense neutron star matter. Calculations are performed in relativistic mean field models in which both the baryon-baryon and (anti)kaon-baryon interactions are mediated by meson exchange. It is found that anti-K⁰ condensation is quite sensitive to the antikaon optical potential and depends more strongly on the nucleonic equation of state. For moderate values of antikaon potential and a rather stiff equation of state, a significant region of maximum mass star will contain anti-K⁰ meson. The critical density of anti-K⁰ condensation is always higher than that of K^- condensation. With the appearance of K^- and anti-K⁰ condensates, pairs of p-K^- and n-Kbar⁰ are produced with equal proportion leading to a perfectly symmetric matter of nucleons and antikaons in neutron stars. Along with K^- condensate, anti-K⁰ condensate makes the equation of state much softer resulting in smaller maximum mass stars compared to the case without any condensate