  In locale theory, a sublocale is said to be remote in case it misses every
nowhere dense sublocale. In this paper, we introduce and study a new class of
sublocales in the category of bilocales, namely (i,j)-remote sublocales. These
are bilocalic counterparts of remote sublocales and are the sublocales missing
every (i,j)-nowhere dense sublocale, with (i,j)-nowhere dense sublocales being
bilocalic counterparts of (\tau_{i},\tau_{j})-nowhere dense subsets in
bitopological spaces. A comprehensive study of (i,j)-nowhere dense sublocales
is given and we show that in the class of balanced bilocales, a sublocale is
(i,j)-nowhere dense if and only if its bilocale closure is nowhere dense. We
also consider weakly (i,j)-remote sublocales which are those sublocales missing
every clopen (i,j)-nowhere dense sublocale. Furthermore, we extend
(i,j)-remoteness to the categories of bitopological spaces as well as normed
lattices. In the class of \sup-T_{D} bitopological spaces, a subset A of a
bitopological space (X,\tau_{1},\tau_{2}) is (\tau_{i},\tau_{j})-remote if and
only if the induced sublocale \widetilde{A} of \tau_{1}\vee\tau_{2} is
(i,j)-remote.
