  We define and characterize the notion of (i,j)-Baireness for bilocales. We
also give internal properties of (i,j)-Baire bilocales which are not translated
from properties of (i,j)-Baireness in bispaces. It turns out (i,j)-Baire
bilocales are conservative in bilocales, in the sense that a bitopological
space is almost (i,j)-Baire if and only if the bilocale it induces is
(i,j)-Baire. Furthermore, in the class of Noetherian bilocales, (i,j)-Baireness
of a bilocale coincides with (i,j)-Baireness of its ideal bilocale. We also
consider relative versions of (i,j)-Baire where we show that a bilocale is
(i,j)-Baire only if the subbilocale induced by the Booleanization is
(i,j)-Baire. We use the characterization of (i,j)-Baire bilocales to introduce
and characterize (\tau_{i},\tau_{j})-Baireness in the category of
topobilocales.
